They come to Jesus by the faith given to them by the indwelling of the Holy Spirit, by which, they come to believe in Him. They don't literally do something to come to Him. When they are given faith, they have come to Him because it is His faith that is imputed to them. It is called becoming saved/born again.
[Gal 5:22 KJV] 22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith,
[Gal 2:16 KJV] 16 Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.
Verse 17:2 explains what you don't see in verse 6:37 - that God gave power over all flesh to Jesus, but only those
of the "all flesh", which God specifically chose and gave to Jesus, will He give eternal life to. No participation on their part necessary, nor possible, nor mentioned. According to those verses, and many other like verses, God and Jesus did/does it all - He simply bestows it upon those whom He saves. So, I think that it is you who is the worker of deception in that you would impose upon those to be saved a task for them to become saved, when no such task exists. According to your "person's part to come" comment, you would have them try to perform a work to complete their salvation, yet the requirement you would impose upon them in order to be saved, comes from Satan, not God. That is why God has told us that we are saved completely by His grace and not by our works or deeds, no matter how seemingly trivial they may be.