In his article, Hamilton does an excellent job of biblically refuting the major Calvinist arguments from the Gospel of John, in particularly John 8:47 and 10:26. He answers the question in context of what it means "to be a child of God, to belong to the Father, and to be one of Christ's Sheep". Hamilton points out that in the Old Testament, that "belonging to God" etc. is used to mean the nation of Israel, but more importantly that it can more specifically refer to the Jews who were repentant and living in right covenant relationship with the Father.
It then makes sense that Jesus' Jewish audience did not believe him, because they did not believe the Father. Jesus' point is that there would not be any Jews still living rightly in the old covenant once the new covenant had been established. People would either accept or reject Jesus, so that there would not be any "third option". All the Jews who were truly repentant would believe Jesus, and God would ensure that none would be lost during this transition.
Hamilton also deals with Calvinist objections and other arguments used by Calvinists from the Gospel of John.