Why do Seventh-day Adventsists believe in a great end of days conflict about the Sabbath day? In an official statement on the Roman Catholic Church, Seventh-day Adventists claim that the Roman Catholic church will be wrapped up in a great conflict about the Sabbath day:


  Adventists believe, on the basis of biblical predictions, that just
  prior to the second coming of Christ this earth will experience a
  period of unprecedented turmoil, with the seventh-day Sabbath as a
  focal point. In that context, we expect that world
  religions--including the major Christian bodies as key players--will
  align themselves with the forces in opposition to God and to the
  Sabbath. Once again the union of church and state will result in
  widespread religious oppression.


What are the "biblical predictions" that this view is based on?
This idea primarily comes from the teachings of Ellen G. White, whom the Seventh-day Adventists consider a modern-day prophet.
Early Writings, p 65:

The pope has changed the day of rest from the seventh to the first
day. He has thought to change the very commandment that was given to
cause man to remember his Creator. He has thought to change the
greatest commandment in the decalogue and thus make himself equal with
God, or even exalt himself above God. The Lord is unchangeable,
therefore His law is immutable; but the pope has exalted himself above
God, in seeking to change His immutable precepts of holiness, justice,
and goodness. He has trampled underfoot God's sanctified day, and, on
his own authority, put in its place one of the six laboring days. The
whole nation has followed after the beast, and every week they rob God
of His holy time. The pope has made a breach in the holy law of God,
but I saw that the time had fully come for this breach to be made up
by the people of God and the waste places built up.

This is based on her interpretation of Daniel 7:25 (ESV):

He shall speak words against the Most High, and shall wear out the
saints of the Most High, and shall think to change the times and the law;
and they shall be given into his hand for a time, times, and half
a time.

In the same vein as many Premillenial Dispensationalists, White identifies the 4th beast in the above passage as the Antichrist who will appear before a great tribulation prior to the return of Christ and a subsequent 1000-year reign.
But although Adventists are not the first regarding the interpretation of the Papacy being identified as the Antichrist (prominent protestants, such as Luther, Calvin, Knox, and others have held that position), they do understand this in the context of what they call the Great Controversy (more on this below).
The important phrase relevant to the question is &quot;shall think to change times and the law;&quot; which is understood to specifically by the Seventh-day Adventists to mean changing Saturday worship (one of the Ten Commandments) to Sunday worship.
There are plenty of SDA books regarding the Sunday/Sabbath conflict, the most important being White's &quot;The Great Controversy between Christ and Satan&quot;, published in 1911. There she also talked about the role of the United States of America in the final conflict (identifying it as the Second Beast of Revelation 13) . This view is also present in other popular, more modern books, like Jan Marcussen's, National Sunday Law.
Some background facts which make this an especially important point to the Seventh-day Adventists:
1. Spirit of Prophecy
Ellen G. White is regarded as the modern day SDA prophet having the &quot;spirit of prophecy&quot; referred to in Rev 19:10. See also Rev 12:17.
This leads the SDA church to regard themselves as a special &quot;last days&quot; remnant (because only they properly keep the commandments) and having their own special revelation (Ellen White's writings).
2. The Great Controversy
The Great Controversy is a very important theme in the SDA church. National Sunday Law (the pope changing the day of worship from Saturday to Sunday) is an acute representation of this larger conflict.  According to the SDA church, Sunday keeping will be forced by civil laws all over the world, separation of State and Church will be lost (even in the USA), and the Papacy will lead the final movement against God's Law.
3. Sabbath Day
Although the Ten Commandments are all of equal importance for the SDA Church, keeping the Sabbath holy is considered of special importance during the final conflict, due to the following reasons:

It's the only Commandment of the Ten that is not universally shared by other Christians, not even Protestants. That will make the Sabbath very difficult keep in the final context described in the Great Controversy.

According the SDA beliefs, God's law must be kept as a whole (whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it - James 2:10). So Sabbath can not be negotiated, not even for the sake of union with other Christian denominations.


For the SDA church, the mark of the Beast during the final days (Rev. 13:16-17) is Sunday's observance, as a system instituted by men (the Papacy), in contrast to God's real Commandments (Sabbath observance).
Conclusion
Put these three facts together, and you get a great end-times controversy over the Sabbath commandment which the faithful remnant follow because they alone have the &quot;Spirit of Prophecy.&quot;