John 6:37 Jesus says:
"All that the Father gives me will come to me, and whoever comes to me I will never cast out."
The verse before this, Jesus said:
"But I said to you that you have seen me and yet do not believe."
A very simple conclusion from John 6 is, if you believe that Jesus is the bread of Life that has come down from Heaven to bring Eternal Life to all who believe, and you'll go to Him - He will never cast you out."
What does it mean to "COME TO" Jesus?
The progression seams to be, first believe and then go. If we join this with Jesus' command to "repent and believe the Gospel"; first we have our mind changed in regard to our sin and God's Righteousness and then we believe the Gospel, we believe in Jesus and trust in Him to save us. That progression would lead us away from sin to to Jesus - if we truly believe we would "go to Jesus".