How do Arminians reconcile free will with God's omnipotence logically? I just finished reading Mere Christianity and was blown away by some of the statements Lewis makes. He mentions "even [God] cannot produce [a changed heart]  by a mere act of power...It is something they can freely give Him or freely refuse Him ." (Mere Christianity Book 3 chapter 10)

This brought up an interesting point in my mind: if you believe in the idea of Free Will with regards to Salvation or a changed heart, you indirectly believe that there is something God cannot do. This directly contradicts the scriptures including Matthew 19:26 and Luke 1:37 ( as well as many others, see http://www.openbible.info/topics/omnipotence) that talk about Gods omnipotence.

I grew up in a Calvary Chapel church where Free will was pushed ad nauseum and I was wondering how these Christians as well as other Arminians reconcile free will with something God cannot do.
Because some things cannot be accomplished by the application of power.

Suppose I asked you to draw a 4-sided triangle. You would presumably reply that this is impossible, because a triangle by definition has only 3 sides. Suppose I then say, Well, what if you had 10 really strong men to help? Then could you do it? Of course the logical reply is that it doesn't matter how much strength or power is available. It is not a question of power, but of logical impossibility.

When we make statements like, "God can do anything", we don't mean that literally. At least, not if we are thinking logically. I remember when I was a kid another kid once asked our Sunday School teacher, "If God can do anything, then can God sin?" The teacher replied, "God does not want to sin." So the kid asked, "But could he sin if he wanted to?"

God cannot make 4-sided triangles. God cannot sin and remain holy. One could come up with many things that God cannot do because they are logical impossibilities, and no amount of power makes them possible because power is irrelevant.

Lest you say, "But the Bible says God can do anything" ... May I point out that the Bible itself says that words like "all" are not always intended absolutely literally. 1 Corinthians 15:27 (NIV), "Now when it says that “everything” has been put under him [Christ], it is clear that this does not include God himself". I presume when Paul wrote, "I can do all things through Christ who strengthens me", by "all" he did not mean that he could fly or see through walls ... or wave his hands in the air and magically cause everyone in the world to come to Christ.