Does God "Draw" Us?

Does God “Draw” Us to Himself?

“No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.” John 6:44
Also:
“’Here are some of you that believe not.’ For Jesus knew from the beginning who they were that believed not, and who should betray him. And he said, ‘Therefore said I unto you, that no man can come unto me, except it were given unto him of my Father.’ From that time many of his disciples went back, and walked no more with him.” John 6:64-66
I've been working on these verses for months. You may want to read more of John 6 to get a better grasp of what was going on when Jesus tells his disciples that no one comes to believe in him and that he is the Son of God unless God "draws" that person. Strong's Concordance defines this word "draw" as "to drag” (literally or figuratively) or "to coil or wrap" or to "take to one's self" as in God taking the person he draws to Himself.
By using this word "draw" I believe Jesus is saying that God must give a person a desire or ability to believe in Jesus which might also mean that some people are not given this desire or ability to believe in Jesus (and specifically who He is- the Son of God).
To show you another example of this "draw" look at Matthew 16:15-17:
He saith unto them, But whom say ye that I am? And Simon Peter answered and said, Thou art the Christ, the Son of the living God. And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.
How about that? Jesus tells Peter that he didn't come to the conclusion that Jesus was the Son of God by himself, but that God revealed or disclosed (per Strong's) this fact to him. Evidence again that there may be some things, including believing that Jesus is the Son of God, that we may not have the intellect to understand without the "draw" or revelation given to us by God.
Here’s one more example that is similar. Remember when Mary Magdalene thought she was talking to the gardener at Jesus’ tomb? Jesus asks her “Woman, whom seekest thou?” And she answers by asking if this gardener had taken the body of Jesus somewhere that she might go and get it. Then Jesus reveals himself to her and she recognizes him as if he had suddenly given her this ability to now recognize him. This seems like the same thing that happened in John 6 and Matthew 16 but this revelation becomes a physical recognition of Jesus rather than a spiritual understanding that Jesus is the Son of God which we can assume Mary Magdalene already believed.
Now, in John 6: 64-66 Jesus repeats again what he said in John 6:44. “Therefore said I unto you, that no man can come unto me, except it were given unto him of my Father.” It sure sounds like Jesus is answering one of my age-old questions: Why do some people believe in Jesus and some people don’t? From these two passages in John, and the supporting verses I’ve included here, it sure looks like the answer is that God doesn’t call every person to him.
To support this theory consider what we know about the Book of Life from Revelations 20. God already knows the names written in the Book of Life, those that will not be cast into the Lake of Fire on Judgment Day. Can we then conclude that God knows whom to call to himself and whom not to call? John 6:64 clearly shows that Jesus knew that Judas would betray him, but also seems to indicate that Judas was not a true believer.
So, then, when we come upon a person who challenges or disputes our Christian principles that Jesus is the Son of God, that He died on the cross and was risen by God from the grave, can we assume that this person either has not yet, or may never be drawn by God to Himself, or perhaps this person has been drawn or called by God, but has failed to answer God affirmatively?