There are several scriptures that illustrate that God draws his elect to him.
These were cribbed from this site
John 6:35-37 States that those the Father gives will come to him. Not that they might come. That they will come.
35Then Jesus declared, “I am the bread of life. Whoever comes to me will never go hungry, and whoever believes in me will never be thirsty. 36But as I told you, you have seen me and still you do not believe. 37All those the Father gives me will come to me, and whoever comes to me I will never drive away.
Romans 8:28-30 Lay out the path to salvation quite clearly. He predestines us, calls us, justifies us and then glorifies us. There doesn't seem to be any doubt that those he predestines will be called, or that those he calls will be justified or those he justifies will be glorified.
28And we know that in all things God works for the good of those who love him, who have been called according to his purpose. 29For those God foreknew he also predestined to be conformed to the image of his Son, that he might be the firstborn among many brothers and sisters. 30And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified.
John 6:43-51 (emphasis mine). This quite clearly says no one comes to Christ except that the Father draws them. (Ref was cribbed from wikipedia)
43“Stop grumbling among yourselves,” Jesus answered. 44“No one can come to me unless the Father who sent me draws them, and I will raise them up at the last day. 45It is written in the Prophets: ‘They will all be taught by God.’ Everyone who has heard the Father and learned from him comes to me. 46 No one has seen the Father except the one who is from God; only he has seen the Father. 47Very truly I tell you, the one who believes has eternal life. 48I am the bread of life. 49Your ancestors ate the manna in the wilderness, yet they died. 50But here is the bread that comes down from heaven, which anyone may eat and not die. 51I am the living bread that came down from heaven. Whoever eats this bread will live forever. This bread is my flesh, which I will give for the life of the world.”
It seems to me that the scriptural proof for needing to be drawn to Christ is pretty clear. However, the Irresistible nature of that drawing power could be questioned. The Romans 8 passage and John 6:37 are clear on this however. Those who are called will be drawn.