The thing that makes this difficult to fathom is the fact that Calvinism teaches that salvation is purely monergistic, that is, independent of anything involving man, and is solely the work of God in bringing about faith. So how would anything get in the way of an alleged Irresistible Grace? Usually what follows is the “predestined means” argument, but think about it. If, as Calvinism teaches, God preemptively removes the old stony heart, and implants a new regenerated heart in order to irresistibly receive Christ, then that person will repent, whether he hears from an Arminian preacher, or a Calvinist preacher. Yet, here is the case that one Calvinist actually lays out:
Does this mean that if man changes the way that he preaches, that God will be liberated to give out more Irresistible Grace? What does this do to the supposed monergistic salvation taught by Calvinists? It simply will not do, to suggest that God ordains the means of salvation, because Noblit went so far as to suggest that Arminian evangelism is “dooming men’s souls.” Is he actually suggesting that this would otherwise not occur, if a Calvinist message was taught instead? The second point is that Noblit applauds the “Evangelism Explosion” of Calvinist, D. James Kennedy, when he points out the inconsistency of non-Calvinists in forgetting about him, when insisting that Calvinism kills evangelism. Yet, he doesn’t seem to realize that D. James Kennedy’s evangelism is very similar to the Arminian evangelism, which he so bitterly condemns as being “wicked,” “a silly superstition” and a “sacrament in Baptist clothes”:
Calvinist, D. James Kennedy, writes: “Our faith and our repentance are the work of God’s grace in our hearts. Our contribution is simply the sin for which Jesus Christ suffered and died. Would you be born anew? There has never been a person who sought for that who did not find it. Even the seeking is created by the Spirit of God. Would you know that new life? Are you tired of the emptiness and purposelessness of your life? Are you tired of the filthy rags of your own righteousness? Would you trust in someone else other than yourself? Then look to the cross of Christ. Place your trust in him. Ask him to come in and be born in you today. For Jesus came into the world from glory to give us second birth because we must--we MUST--be born again.” (Why I Believe, p.140, emphasis mine)
Again, this is an example of a Calvinist who is preaching that lost people can and must call out to God and pray that He makes them Born Again. However, Calvinism teaches that a totally depraved person cannot make this prayer unless he has already been made preemptively Born Again. So you can see that Calvinistic theology is in a bit of disarray.
Consider another matter, in which Calvinists not only, openly oppose Alter Calls and Gospel Invitations, but also denounce prayers of invitations to ask Jesus into a person’s heart. Here is a link to a Blog discussion on that point.