Irresistible Grace & Effectual Calling

The Bible "locates unbelief in the total inability of sinners to effect their own liberation from the bondage of the will, and ... locate faith in the unconditional election, redemption, and effectual calling of the triune God alone. God gives not only sufficient grace (that is, enough grace to enable sinners to respond positively to God if they choose to do so), but efficient grace (that is, regeneration as well as faith and repentance as gifts)." 
- Michael Horton The Christian Faith, pg. 562

Regeneration is a secret act of God in which he imparts new spiritual life to us. As the gospel comes to us, God speaks through it to summon us to himself (effective calling) and to give us new spiritual life (regeneration) so that we are enabled to respond in faith. Effective calling is thus God that Father speaking powerfully to us, and regeneration is God that Father and God the Holy Spirit working powerfully in us, to make us alive.

Sometimes the term irresistible grace is used in this connection. It refers to the fact that God effectively calls people and also gives them regeneration, and both actions guarantee that we will respond in saving faith. The term irresistible grace is subject to misunderstanding, however, since it seems to imply that people do not make a voluntary choice in responding to the gospel - a wrong idea, and a wrong understanding of the term irresistible grace. The term does preserve something valuable, however, because it indicates that God's work reaches into our hearts to bring about a response that is absolutely certain - even tough we respond voluntarily.

Wayne Grudem from Systematic Theology (pg. 699)

“You stiff-necked people, uncircumcised in heart and ears, you always resist the Holy Spirit. As your fathers did, so do you” (Acts 7:51). This passage, which is often used in an attempt to refute the biblical doctrine of irresistible grace, actually supports it. Notice the condition of the persons who are doing the resisting: their hearts and ears are uncircumcised, which is the Bible's way of saying they are unregenerate or unspiritual. A person in this condition will always resist the outward call of the gospel. The Holy Spirit may convict them of sin and work to show them their need to Christ, but as long as they remain unregenerate, their hearts will remain closed to Christ. Irresistible grace does not mean that whenever the Spirit works He is irresistible. Rather, it means that while His promptings are always resisted by the dead in sin, He can make the gospel irresistible when He opens their spiritually blind eyes, when he opens their deaf ears and turns their heart of stone to a heart of flesh. He quickens us while we are dead, which is no work of man. As Ephesians 2:5 says, “Even when we were dead in our trespasses, [He] made us alive together with Christ--by grace you have been saved.”