Faith is in man's reach. Romans 10:17 says that faith comes from hearing the word of God and we all can choose what we listen to. John 20:31 gives a similar message. I argue that the gift of God in Ephesians 2:8 is salvation, not faith, based not only on Romans 10:17, but also upon Ephesians 2:9 and Romans 6:23.
Romans 10:17 So then faith comes by hearing, and hearing by the word of God.
John 20:31 But these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name.
Total Depravity: Calvinists believe man is too morally depraved to repent and trust.
For Calvinists who wish to promote a doctrine of Total Inability, there is good and bad news. The good news is that it really is a doctrine found in the Bible. The bad news is that it reflects the doctrine of unrepentant Israel, which doctrine, God repudiated:
Jeremiah 18:11-13: “‘So now then, speak to the men of Judah and against the inhabitants of Jerusalem saying, “Thus says the Lord, ‘Behold, I am fashioning calamity against you and devising a plan against you. Oh turn back, each of you from his evil way, and reform your ways and your deeds.’” But they will say, “It’s hopeless! For we are going to follow our own plans, and each of us will act according to the stubbornness of his evil heart.” Therefore thus says the Lord, “Ask now among the nations, who ever heard the like of this? The virgin of Israel has done a most appalling thing.”’”
God's Sheep. The Calvinist perspective is that God chooses His own sheep, that is, He seeks them and finds them, and has chosen them from eternity past.
God indeed seeks the lost, but the objection is over the notion that God makes the choice for us. Instead, we must choose God over sin. In other words, if you were to ask God to give you an “Irresistible Grace” so that you would never sin again, ever—you won’t get it. Like Peter, you will fall, and get back up again, and you must choose God over sin, every day. It’s the struggle that everyone faces. Some people don’t want to let certain things go. Others fall back into the same sins over and over, but we must get back up again. We must choose. We have to make a choice. He won’t make it for us.
Thankfully, because we have turned to God, He has given us a new nature that seeks to walk with Him and to do His will. One example of this in the NT is where Peter promises salvation (i.e. forgiveneness of sins and receiving the Holy Spirit) to those who respond in repentance and baptism in Acts 2:36-41.