What is the Biblical Basis for differences in the Dispensational and Non-dispensational understanding of the 70th week in the Book of Daniel? I've heard at least two different interpretations from Baptists of: 


  And he shall confirm the covenant with many for one week: and in the midst of the week he shall cause the sacrifice and the oblation to cease, and for the overspreading of abominations he shall make it desolate, even until the consummation, and that determined shall be poured upon the desolate.
  
  Daniel 9:27 - KJV


referring to one of these:


Non-dispensational view: 

The period of the 1st Jewish war (approx 66 to 73AD), when the sacrifices were stopped mid way and the temple was destroyed in 70AD. 
Dispensational view:

The 70th week represents the time of Jacob's trouble and when the anti-christ comes and makes a peace covenant with the Jews, but breaks it half way through. 


What is the scriptural basis for these interpretations?
There isn't really a single "Baptist view" or even just two or three Baptist views which are in any way distinctive from the views of other major Christian groups/denominations. The following I summarise from Edward J Young's commentary.

There are two broad interpretations - Non-Messianic Interpretations (NMI), and Traditional Messianic Interpretations (TMI).

NMIs mostly tend to focus on Antiochus Epiphanes as the subject of the prophecy: such a focus goes back at least as far as Julius Hilarianus towards the close of the 4th century. An NMI position is adopted by M. Stuart (1850), J.D. Prince (1899), S.R. Driver (1922), J.A. Montgomery (1927)(International Critical Commentary) (which E.J. Young says is very worthy for its philological content). A modern advocate of an NMI is Chris White (2013). "The Septuagint Translation also, by means of additions to the text appears to interpret the passage the same way." (E. J. Young, page 192).

Your question relates to differences between the Dispensational and Non-Dispensational interpretations of the passage. Since both these interpretations are TMIs I will leave the NMIs at that.

Traditional Messianic Interpretations, TMIs, go back at least as far as Augustine. TMIs regard this passage as a prophecy of the first advent of Christ in the flesh, the central point of which is his death, and they relate the prophecy also to the destruction of Jerusalem by the Romans.

Before Augustine, Josephus, the Jewish first century historian, although he did not relate it to Jesus of Nazareth as the Messiah, he did relate the prophecy to the destruction of Jerusalem by the Romans:-

"In the very same manner Daniel also wrote concerning the Roman government, and that our country should be made desolate by them." (Antiquities, book 10, ch 11, [three quarters down] paragraph 7).

The Dispensational View was promoted by Harry Ironside in his book "The Great Parenthesis" (publ. 1943), the parenthesis being between the end of the 69th week and the beginning of the 70th week which has so far lasted 2000 years or so. In addition, before Ironside's work the Scofield Reference Bible (first publ. 1909 and then updated by author and re-publ. 1917) was and is effective in making this interpretation popular. Before the Scofield Reference Bible, the Ultradispensationalist (Bullingerist) Sir Robert Anderson, had produced his work "The Coming Prince" (1894). These works all point to 445 BC as the starting point. Before Robert Anderson, Ernst Wilhelm Hengstenberg, a staunch defender of the Faith, and author of many commentaries, had written his commentary on Daniel in German (1831) with a following English translation (1848): Hengstenberg also believed the starting point was 445 BC. A further translation of Hengstenberg's book was produced by James Martin and included in "Christology of the Old Testament" (1858). From this stable of interpretation came the idea of a prophetic year of 360 days. Because these interpretations have Jesus of Nazareth as the focal point of the prophecy they are a variant of the TMI.

I will return later to what I believe are major problems with this interpretation.

Then there is an essentially amill minority view which hold all the numbers of weeks to be figurative or symbolic numbers such as two German authors C. F. Kiel, (English translation 1877). and T. Kliefoth "Das Buch Daniel" (1868). I shall not comment on this interpretation because I feel it vanishes away immediately a better interpretation is seen, at least for Protestant amillennialists.

Then there are amillennial interpretations which also have multiple variations but certain common themes apply to many of them. I shall give an amillennial view below.

One of the salient differences between Amill and Dispensational views is the interpretation of the 1 week following the 62 weeks.

In the (non-symbolic) amill view there are essentially two prophecies in the passage:

The first prophecy is of 70 weeks, each week being 7 years. It terminates in the most important event in world history up to the present time, and relates to the Messiah's first advent.

The second prophecy is of 7 weeks, 62 weeks and 1 week. It has a different termination point: its termination point is the most important event yet to happen in world history and relates to the Messiah's second advent.

The second prophecy has the same starting point as the first prophecy, and each week is the same length as the first prophecy, EXCEPT for the final week. This second prophecy has a single theme: if you like, for 7 weeks a tap is switched on, then for 62 weeks the tap is switched off, then for the final week the tap is switched on again. It has the grandest theme imaginable and divides the future of the world history into, spiritually speaking, the most significant periods it is possible to conceive.

Then any amillennialist would be willing to look at the prophecy as having a double meaning: there is a physical, earthly Jerusalem in the Middle East and there is a heavenly Jerusalem, the City of God, the elect people of God, all those predestined to have faith in the Messiah. The word to rebuild relates to both the earthly Jerusalem and the heavenly. The heavenly Jerusalem was made possible by what happened at the end of the 70 weeks; and the heavenly Jerusalem will be finally finished, and the decree to build will reach its culmination, at the end of the 7, 62 , and 1 week, when all the elect people of God will have been gathered into the Kingdom of God, into the heavenly Jerusalem.  The city will have been finally built.

I think it must be admitted that it is one of the greatest of oddities in the interpretation of the Scriptures that the year 458 BC was so easily rejected by commentators and expositors for such a long time despite the fact that 458 BC is exactly 490 years prior to the year of the crucifixion (if we take 33 AD as the year) and amazingly close to 490 years if we take 30 AD as the year of the crucifixion. Surely the decree given 458 BC should have been given the most exact scrutiny, no stone, no pebble should have been left unturned until this possible starting point had been thoroughly credited or discredited. As I read Edward Young's book it is hard to see that this examination was ever done, but rather it seems the date was thrown overboard with indifferent enthusiasm!

An example of such a rejection can be seen in Harry Ironside's comments on chapter 9 at https://www.studylight.org/commentaries/isn/daniel-9.html
"Some insist that the reference is to the commandment given in the seventh chapter of the book of Ezra, which was approximately 457 B.C.; but a careful examination of that decree will make it evident that it did not really have to do with restoring and building the city of Jerusalem at all, but was rather a confirmation of the earlier decree of Cyrus to rebuild the Temple and reinstate the worship of God in Israel. It seems far more likely that the commandment referred to is actually that given in the second chapter of the book of Nehemiah. There we have in very truth a commandment to restore and build Jerusalem, and that commandment was given about 445 B.C."

That summary dismissal of 457 BC is all the comment you get about that year from Harry Ironside. He is not alone. Edward Young, an amillennialist, does worse: his commentary (published 1949) doesn't mention 457 BC (or 458 BC) at all. This is despite the fact that he references the works of 65 different authors, of ALL doctrinal hues, in his bibliography and, in passing, seeks to produce a brief summary of their views. (Despite this rather glaring omission it is still a very useful commentary (in my opinion), even for this passage, not least because of his knowledge of Hebrew.)

This is all very strange: if we simply follow our nose 490 years before the crucifixion we arrive at 458 BC and the decree of Artaxerxes I in Ezra 7:7. Once we have 458 BC I believe the rest of the prophecy begins to fall into place.

To summarise the history: Jerusalem and its temple were destroyed by the Babylonians in 587 BC.

In 539 BC Cyrus conquered Babylon, and very early in his rule, about 539 BC, he decreed that the Jews could return and rebuild in order to restart the Temple worship (Ezra 1:1-11). This decree was re-issued by Darius I, about 522 BC (Ezra 6:1-15). Again the decree was re-issued by Artaxerxes in 458 BC (Ezra 7:7 see also 7:13) leading to the return of Ezra. Some have claimed another decree was given by Artaxerxes at the time of Nehemiah's return, 445 BC.

The Persian Kings are:-

Cyrus the Great 539 - 530 BC (began to reign Persia in 559, but 539 he conquered Babylon, and thus Judaea)

Cambyses II 530 -522

Bardiya/Smerdis/Gaumata 522 ("the imposter")

Darius I (Hystaspes) 522 - 486

Xerxes (Ahasuerus) 486 - 465 (husband of Esther, the 4th king of Daniel 11:2)

Artaxerxes I 464 - 424

Darius II 423 - 404

Artaxerxes II 404 - 358

Artaxerxes III 358 - 338

Artaxerxes IV 338 - 336

Darius III 336 - 330

Artaxerxes V 330 - 329...

And after them Alexander the Great.

Nehemiah returned to Jerusalem and rebuilt the walls in the 20th year of Artaxerxes (Neh 2:1) which was Artaxerxes I, 445 BC. His second journey to Jerusalem was during or not long after the 32nd of Artaxerxes, 433 BC, (Neh 13:6).

One of the most difficult parts of the prophecy has been the meaning of the 7 and 62 weeks. Here I venture the only realistic interpretation: the 62 weeks, 434 years, is the period of prophetic silence between the completion of the Old Testament and the beginning of the ministry of John the Baptist.

Is there any evidence for this? I believe there is.

Elephantine Papyri B19 (Cowley 30) was written 25 November 407 BC and refers back to a previous letter written to "Jehohanan the High Priest" about 410 BC.
If you google search "Baytagoodah" and "elephantine papyri" and go down to letter B19. Go down to page 142 and read the Appeal section.

This letter shows that Jehohanan ("Jonathan" in Nehemiah 12:8, and "Johanan" in Nehemiah 12:22) was High Priest in 410 BC and probably later up to maybe 407 BC.
Yet Nehemiah 12:22 indicates Jaddua (the son of Johanan) was High Priest at the time of composition of chapter 12 of Nehemiah.

Nehemiah 12:22 also mentions the reign of Darius the Persian. This is Darius II who reigned 423 to 404 BC. So clearly Nehemiah was written after 423 BC, but the mention of Jaddua as High Priest means Nehemiah was written after 410 BC when the Elephantine Papyrus says Jehohanan was High Priest.

So sometime after 410 BC Jehohanan died, Jaddua became High Priest in his place, the book of Nehemiah was written, and then Darius II died in 404 BC.

In summary we have a window from 410 BC to 404 BC when the book of Nehemiah was written and added to the Scriptures. This, I believe, is the meaning of the 7 weeks and the 62 weeks.

The 7 weeks is the period from 458 BC to 408 BC when there was still the word of God being proclaimed and when there were still living divinely appointed prophets in Judah.

The 62 weeks is the period starting from the completion of the Old Testament, with the completion of the book of Nehemiah, to the beginning of the ministry of John the Baptist, sometimes referred to as the "Period of Prophetic Silence". It is a distinct period where the beginning and the end of the period are linked together by a common theme.

458 BC of Ezra 7:7 is the anchor of the whole prophecy. 7 weeks from there gives 409 BC, 62 weeks from there gives 26 AD. I suspect that the truly accurate period to the exact year is the 70 weeks up to the crucifixion. (The 7 weeks and 62 weeks do not demand exact years.)

The problem with arguing that the 7 weeks is the period of rebuilding is simply that it is impossible to demonstrate a fulfilment: when can anyone say the year in which a destroyed city was rebuilt? London, Hamburg and Berlin were badly damaged in World War II, but how can anyone say the year in which they were rebuilt? They were reconstructed over many years, and there was never a year when anyone could say they were finished.

"Know therefore and understand that from the going forth of the word to restore and build Jerusalem unto the Messiah the Prince shall be seven sevens, and threescore and two sevens". Those Bible versions which separate the sixty two sevens from the seven sevens (such as the Revised Standard Version) are following the Masoretic Hebrew Text. The RSV says:-

"Know therefore and understand that from the going forth of the word to restore and build Jerusalem to the coming of an anointed one, a prince, there shall be seven weeks.  Then for sixty-two weeks it shall be built again with squares and moat, but in a troubled time".

The Hebrew Masoretic text upon which the RSV depends was produced by Jews in about the 10th century AD. It is easy to imagine this was a deliberate corruption: they deliberately wanted to separate the two periods so that they did not add up to 69 weeks or 434 years: they did not want the prophecy to point to Jesus of Nazareth as the Messiah. It is also worth remembering that by the time of the Masoretes the Hebrew language was virtually a dead language, even to them.

Edward Young, a scholar in Hebrew, in his commentary on Daniel writes:- "At any rate, this violent separation of the two periods is out of harmony with the context. Furthermore, I question whether it is really in accord with the rules of Hebrew syntax to render "(for the space of ) sixty-two sevens," i.e. as an accusative of duration... It is best, therefore, to understand the text as stating that between the terminus a quo and the appearance of an anointed one, a prince, is a period of 69 sevens which is divided into two periods of unequal length, 7 sevens and 62 sevens."

"The streets shall be built again, and the wall, even in troublous times", is referring to the rebuilding of the city, but it need not be declaring the date of such rebuilding. It is like a clue for a cryptic crossword. In truth, it is referring to the book in which these things are written about - i.e. the book of Nehemiah - and the prophecy is referring to the date when that book was completed and added to Scripture.

Why must it be referring to the date of writing? It is because the events within the book of Nehemiah had already happened a few decades before the 7th week after 458 BC. It is not necessary to read into Daniel 9:25 that the city will be rebuilt or completed 49 years after 458 BC.

"the people of the prince that shall come" - the Romans, they "shall came" and destroy the city and the temple, which they did in 70 AD.

"He shall confirm the covenant with many for one week" - this is referring to the Covenant of Grace. It is not talking about any new covenant, or any covenant distinct from the covenants already spoken of in Scripture. The covenant will merely be confirmed, not created... it will be no new, separate, distinct, covenant. It is simply saying that many shall be saved in this final week.
This final week is the entire Gospel Age. 

Why is it only one week? This is because the Father does not want us to know its true length, "it is not for you to know the times or the seasons which the Father has put into his own power" Acts 1:7. The date of the Day of Judgement was not revealed to Daniel or to any other prophet nor even to the Son himself (Mark 13:32). Of course, in Jesus's divine nature as God Jesus knew, but Mark 13:32 tells us in His human nature as man Jesus did not know. Furthermore the end of the world COULD have come a week/seven years after the crucifixion. The Word of God urges us to be always ready, "for you do not know what hour your Lord doth come" (Matthew 24:42).

In short, if the prophecy of Daniel 9 24-27 had finished with 500 weeks rather than 1 week would you have thought it needful for you personally to be "always ready for you know not the hour"?

Finally, some typically amillenial objections to the Dispensational interpretation:-


The Dispensational view requires a break between the 69th and 70th week of some 2000 years or about 285 weeks of years. This alone must be an entirely fatal flaw to the interpretation.
The idea that some of the prophecy relates to the Antichrist has very little within the text to support it. And besides that it means that none of us need be ready (for we do not know the hour our Lord doth come (Matt 24:44)) until after we have seen the fulfilment of this prophecy, until the Antichrist has come: I mean, we can all sit around and do just as we please, because we know Christ will not return to judge us until after the appearing of the Antichrist. Introducing another event, the coming and reign of the Antichrist, before Christ's return is contrary to Matthew 24:37-51.
It seems unlikely, to say the least, that there would be such a cryptic prophecy about, or would include, such a minor detail as the coming of the Antichrist. This prophecy must surely be about things major.. the general periods of the future when, and how, God shall deal with mankind; the death of Christ; the gospel age; the end of the function and purpose of the temple because Christ, the effective sacrifice for sin, has made the temple obsolete, and this, in turn, means the end of the centrality of the Jewish nation in God's dealings with mankind because no temple means no more God-ordained Jewish religious system, whose sacrifices will have finally permanently ceased "even until the consummation", that is until the Day of Judgement.  From an amillennialist's point of view the Dispensational interpretation turns this prophecy on its head: for the amill, the prediction here is that the Temple finally ceases forever, terminating in the 1st century, and so God's special dealings with the Jews finishes forever, but the Dispensationalist view sees this as a prophecy that the Temple will make a come back and the Jews continuing to have a very special place in God's purposes.
The order in which things are spoken in vv26 and 27 shows that "Messiah shall be cut off" (AD 33) after the 62nd week, which means this falls within the final 1 week. The destruction of the city and the temple shall also be within the 1 week (70 AD). It follows that the 1 week is not a seven year period. "And he shall confirm the covenant with many for one week" - this must relate to a covenant with which we are already familiar, not any new covenant. The most obvious reading is that it is the covenant of grace, firstly because we are familiar with that covenant and secondly because it is a very major theme of scripture, and not a trivial detail such as a covenant between the Antichrist and a people.
Our Lord Jesus speaks of the prophecies of Daniel in Matthew 24:15 and Mark 13:14. These are parallel passages. Matthew Henry's commentary has a sufficient interpretation of Chapter 24, which is roughly this:- the apostles think the temple will be destroyed towards the end of the world. The Lord Jesus does not say they are wrong because he himself does not know when the end of the world will be (Mark 13:32), but he asserts there is no necessary connection between the destruction of the temple and the end of the world. Sometimes in the is passage He speaks of the end times, and sometimes He speaks of the time of the destruction of the Temple. In Matthew 24:33-36 notice that He speaks of "THIS generation"/"THESE THINGS" and then, in contrast, He speaks of "THAT day" - "this"/"these" refers to the time of the temple destruction, "that" refers to the end times. And He finishes the whole discourse with a warning that we should always be ready. 
The warnings relating to the book of Daniel are local to the land of Judaea and to Jerusalem, "then let them which be in Judaea flee into the mountains", because it is a local judgement, and an approaching judgement - "THIS generation shall not pass, till all THESE things be fulfilled" (Matt 24:34) - being spoken of.  But of the Day of Judgement, He says "But of THAT day knoweth no man, no, not the angels of heaven, but my Father only".  Christ told his disciples that the prophecy of destruction in Daniel 9:26 would be fulfilled shortly after his crucifixion, before "this generation", the generation standing before him, "passes away".