No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day. (John 6:44)However, John chapter 3, especially the most famous verse of all, John 3:16, is often seen as neutral or even slightly anti-Calvinistic.
In fact, however, John 3 is one of the strongest Calvinistic passages in the New Testament.
In John 3, we have the fascinating dialog between Jesus and Nicodemus. Here, in verse 3, Jesus tells Nicodemus: "I tell you the truth, no one can see the kingdom of God unless he is born again."
This is a universal negative. If you have not been reborn, then under no circumstances can you see the kingdom of God. So you cannot be reborn as a consequence of seeing the kingdom of God—that's backwards, plain and simple.
Jesus then adds a clear explanation that you, as person, have nothing to do with this rebirth:
"I tell you the truth, no one can enter the kingdom of God unless he is born of water and the Spirit. Flesh gives birth to flesh, but the Spirit gives birth to spirit. You should not be surprised at my saying, 'You must be born again.' 8The wind blows wherever it pleases. You hear its sound, but you cannot tell where it comes from or where it is going. So it is with everyone born of the Spirit." (John 3:5-8)This birth is of the Spirit, and it occurs not where it has been earned, but wherever the Spirit pleases. The metaphor of the wind is meant to show that you don't see it coming, and don't know where it is going. No weather forcasting is possible. You can't look at someone and say: "He is about to be reborn, I can tell." Uh-uh. In that circumstance, you should probably say: "I think he has been reborn."
We then have the famous John 3:16, that tells us that believers have eternal life.
But you cannot believe what you cannot see, Jesus tells Nicodemus in verses 12 and 13: “I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things? No one has ever gone into heaven except the one who came from heaven—the Son of Man”.
There is, it seems to me, only one way to wrap your arms around all these verses. Only one logical progression.
If we are not reborn, we cannot see the kingdom of God. If we cannot even see the kingdom of God, we cannot believe. If we cannot believe, we cannot possess eternal life. To me this clearly precludes the logical chain as seen by Arminians: Believe and you will be born again and have eternal life. That can't work—because you can't believe what you can't see, and the once-born are blind.
But John 3 doesn't ever say believe and you will be born again. It teaches believe and you will have eternal life. And it teaches that you must be born again to see the kingdom of God, and seeing the kingdom of God is necessary for you to believe, and when you believe, you have eternal life. The start of the chain—before you have done your part (believe)—is to be born again.
That's textbook Calvinism, and that is what John 3 teaches.