This idea is never presented in scripture. Prevenient grace is a misunderstanding of common grace. Saving grace is never resisted.
This idea of prevenient grace giving everyone a choice goes contrary to Jesus' own words and if reconciled with Jesus' words leads only to universalism or makes Jesus a liar. To say that God gives everyone a faith to believe is to say Jesus fails in his promise of raising up all those up that the Father has drawn.
35 Jesus said to them, “I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst. 36 But I said to you that you have seen me and yet do not believe. 37 All that the Father gives me will come to me, and whoever comes to me I will never cast out. 38 For I have come down from heaven, not to do my own will but the will of him who sent me. 39 And this is the will of him who sent me, that I should lose nothing of all that he has given me, but raise it up on the last day. 40 For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.”
Jesus makes a point here that they have seen him and don't believe because only those the Father has given to him will come to him. If God draws all men, Jesus is obligated to save all those drawn:
43 Jesus answered them, “Do not grumble among yourselves. 44 No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day. 45 It is written in the Prophets, ‘And they will all be taught by God.’ Everyone who has heard and learned from the Father comes to me— 46 not that anyone has seen the Father except he who is from God; he has seen the Father.
Two choices here. Either God draws all men and grants all men faith, which obligates Jesus to save every last man, woman, and child (universalism), or the alternative, Jesus is lying.
The view you present is Pelagian and not biblical.