A major problem for the doctrine of Irresistible Grace is that Scripture explicitly tells us that we can, indeed, resist God's grace. How? By telling us that some people did. In Luke 7:30, we read "But the Pharisees and lawyers rejected the counsel of God against themselves, being not baptized of him." More modern translations than the KJV render this along the lines of they rejected God's will/purpose for themselves.
At this point, Calvinists may object by claiming that if these people genuinely had resisted God's will, they must be greater than Him. Evidently, this is impossible, and so this interpretation is, itself, rejected. Here's the problem with this: We know for a fact that mankind can "overcome" God if He allows them to.
As I wrote those words, I could feel a disturbance in the Force, as if a thousand Calvinists in the future could reach through time and burst my eardrums with loud charges of heresy and blasphemy. But tell me, my Calvinist friends, did God not hang on a cross? I do not feel I should have to defend the deity of Christ to a Calvinist, and so they must answer that yes, He did. And so the next question is why?
The answer, of course, is because He willed it. But did He? Let us hearken back to the Garden of Gethsemane, where Jesus, dreading the pain He would soon endure, cried out to the Father. In Matthew 26:39, we read that Jesus "...fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt."
Suddenly, things seem rather complicated. First off, we see that Jesus has a separate will from the Father. Jesus, for obvious reasons, would prefer another solution to sin than the cross. The Father, by contrast, desires it. Now, I cannot imagine the Father was especially thrilled by the cross either, but ultimately, this shows that God can have two conflicting desires at once. On the one hand, He desired an alternative to the cross. On the other hand, He desired the cross.
But beyond this, we see that while Jesus willed not to go to the cross, man did. And man put Him there. How? Obviously, not by overpowering Him. Christ Himself said "Thinkest thou that I cannot now pray to my Father, and he shall presently give me more than twelve legions of angels?" (Matthew 26:53). If not for God's will, it would have been 100% impossible to nail Jesus on that cross. But He hung there, and men hung Him there, and He even died. Jesus Christ, who made everything that was made, became obedient to death. Was He defeated?
No sane Calvinist would answer in the affirmative. Jesus allowed Himself to be crucified, because although He willed not to be crucified, He also willed to obey the Father. Is it, therefore, unfathomable that when God says He wills all men to be saved (1 Timothy 2:4), He actually means it, but just as He allowed men to nail Him to a cross, He also allows them to reject the grace He offers through it? If Christ was not defeated by Rome, or by Israel, then God was not defeated by Hell. Only if you contend that a mere centurion is greater than God can you also say that men who resist God's grace would be greater than Him also. Thus, we are permitted to interpret Scripture as plainly written: Man can resist God's grace, and it is not He who is defeated, but the fool who does indeed resist Him.