What is the Biblical basis for a resistable enabling (prevenient) grace? I see a few different uses of the term prevenient grace in questions here, so I will define what I meant first: a belief held by traditional Baptists and other non-reformed evangelicals, that though we are all totally depraved and unwilling to come to Christ on our own free will, God gives us a enabling grace that allows us to come to regeneration and faith. But this grace can be resisted and ignored.

What is the Biblical basis for this type of grace?
The doctrine of Prevenient Grace is seen by those who adhere to it as a natural outcome of sound Biblical exegesis.  

In one respect it's akin to the doctrine of the Trinity in that it resolves apparent discrepancies.  With the Trinity, we have clear teachings in Scripture that there is only one God, other clear teachings that Jesus is God, and others supporting that the Holy Spirit is fully God.  

To answer this fully is going to take a bit of time, so I'm going to break this down into three sections:  Principles that are used when looking at these Scriptures, the supporting Scriptures, and the application of the principles that lead to the conclusion of Prevenient Grace.



Principles


The doctrine of Scripture as the inspired inerrant, infallible Word of God.
Rules for resolving apparent Biblical discrepancies.


To understand how Prevenient Grace is drawn out of the texts, you need to start by bearing in mind that to these groups, there can be no question that the Bible is inspired, inerrant, and infallible.  In other words, it was written by God Himself, using the authors as instruments, and therefore not only does not contain errors, it cannot contain errors. This means that it cannot have contradictions.  Something cannot be logically true and false at the same time.  Two polar opposite views that contradict each other cannot be true.

Next, you need to understand that if the Bible contains apparent contradictions, then either the bible is not inerrant, or there's a way to resolve the apparent discrepancy.



Supporting Scriptures

The supporting Scriptures here are, interestingly enough, the ones that show the apparent discrepancy:

The verses that support the Calvinistic view that man plays no part in his salvation, or choice are already documented in many questions on this site:


What is the Biblical basis for Total Depravity?
What is the Biblical Basis for Irresistible Grace?
What is the Biblical basis for Limited Atonement?
What is the Biblical basis for Unconditional Election?


If you take the time to go through the above questions and the answers, the support for the idea that man has no choice in his salvation, and that God chooses who will be saved is overwhelming.  

However, on the other side, there is also overwhelming Scriptural support for the idea that we must choose to accept God's free gift of salvation - in other words, man does play a part.  (Emphasis mine in the following verses)


Matthew 16:24 - Then said Jesus unto his disciples, If any man will come after me, let him deny himself, and take up his cross, and follow me.
John 3:16 -  For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
John 11:40 - Jesus saith unto her, Said I not unto thee, that, if thou wouldest believe, thou shouldest see the glory of God? 
John 7:37 - In the last day, that great day of the feast, Jesus stood and cried, saying, If any man thirst, let him come unto me, and drink.
Romans 4:24 - But for us also, to whom it shall be imputed, if we believe on him that raised up Jesus our Lord from the dead;
Matthew 11:28-30 - Come unto me, all ye that labour and are heavy laden, and I will give you rest. Take my yoke upon you, and learn of me; for I am meek and lowly in heart: and ye shall find rest unto your souls.  For my yoke is easy, and my burden is light.
John 6:40 For my Father’s will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise them up at the last day.”
Revelation 22:17 - And the Spirit and the bride say, Come. And let him that heareth say, Come. And let him that is athirst come. And whosoever will, let him take the water of life freely.


I'm going to stop there.  A comprehensive list is far too long for an answer here, and that's enough to make the point:  There is Scriptural support for the idea that man does have to choose to follow Christ, and that the choice does exist.  It is real.

Taking one more tiny (well, maybe not so tiny since it's the central point of all Christianity) piece of evidence into account... Since man cannot save himself, God provided the payment for our sins.  

In other words, when man is incapable. God provides a way...



Application of the Principles to the Scriptures to draw out the Biblical Concept

Thus far, we've established the following two opposing facts:


Scriptures clearly teach that man is fully depraved and utterly incapable of choosing to follow God.
Scriptures clearly teach that we must choose to follow God, that the choice is ours to make.


Therein lies the conflict.  Do we have a choice or don't we?  Are we capable of choosing or aren't we?  

There is one other conflict that ties in here, for which I haven't provided the Scriptural arguments, but which bears on this topic:  Does God want only certain people to be saved, or does God desire that all would come to Him?.  

Assuming that God's Word is true and that he desires that all come unto repentance...

Scriptural facts:


God wants us all to be saved
we are totally depraved. 
We cannot choose to follow God unless He calls us
We cannot be saved unless we choose to follow God.
God always provides a way


Can be rephrased as... 


  God desires that all be saved, and he teaches that it's our choice to do so.  He doesn't force us.  But because we are totally depraved,
  we cannot choose to follow God.  we are utterly incapable.  Since we
  cannot choose to follow Him on our own, but He expects us to choose, 
  He provides a way that allows us to choose to follow God.  He calls us
  first and gives us the previnent grace to choose to obey His perfect
  will.


...with no conflicts and no leaps of logic.