Part of the problem in discussing Irresistible Grace is that each side defines it differently.
Non-Calvinists (at least some in this threat) define it as God's forcing people to believe, in violation of their free will. Or, God's saving people who don't want to be saved.
I like John Piper's definition:
The doctrine of irresistible grace means that God is sovereign and can overcome all resistance when he wills. "He does according to his will in the host of heaven and among the inhabitants of the earth; and none can stay his hand!" (Daniel 4:35). "Our God is in the heavens; he does whatever he pleases" (Psalm 115:3). When God undertakes to fulfill his sovereign purpose, no one can successfully resist him.
Here's another Piper quote from the same article (part of a series of articles on the five points of Calvinism, carried on his website, desiringgod.org)
More specifically irresistible grace refers to the sovereign work of God to overcome the rebellion of our heart and bring us to faith in Christ so that we can be saved. If our doctrine of total depravity is true, there can be no salvation without the reality of irresistible grace. If we are dead in our sins, totally unable to submit to God, then we will never believe in Christ unless God overcomes our rebellion.
I'm sure we all have prayed for God to save someone. Many of you have prayed fervently and continually for the salvation of a loved one, a friend, etc. Implicit in your prayer is the recognition that God has the power to save. Otherwise, the prayer is pointless.
I've heard non-Cals pray, "Lord, open his eyes, convict him of his sin. Oh God, please save him." So both views believe God acts first in connection with salvation.
Calvinists may also pray, "Lord, change his heart; make him willing." Non-Cals dare not pray that way, for that would be asking God to violate his free will, and we can't have that.
I've heard some non-Cals pray "Lord, touch his heart." What do they mean by that? What do they want that touch to accomplish? A change of heart? A unilateral act of lthe Holy Spirit to effect a change of heart? A forced change of heart? On someone who otherwise doesn't want to be saved?
Why pray for God to save someone if He can't, unless given permission?
A lot of you have a heavy burden for the lost in general, and some individuals in particular. Some of you are preachers, some are missionaries, some are just lay folks who have faithfully given a witness to the gospel. And you have cried out to God for their salvation.
Why would you not pray, "Oh Lord God, do whatever it takes to bring him to salvation. Open his eyes, change his heart, show him his sin, make him hate it, make him repent, give him faith--anything, Lord, just please save him."?
I can hardly imagine anyone praying, "God, please save my son--but not if he doesn't want it. Lord, save him, but don't violate his free will."
We who have lost loved one should be for irresistible grace, not against it.