This question is at the very heart of the difference between Catholics and Protestants.Precisely!
Indeed. I would suggest other parts of John 6 are more of the heart of the difference between Catholics and Protestants:
Joh 6:45 It is written in the prophets, And they shall be all taught of God. Every man therefore that hath heard, and hath learned of the Father, cometh unto me.
Joh 6:64 But there are some of you that believe not. For Jesus knew from the beginning who they were that believed not, and who should betray him.
Joh 6:65 And he said, Therefore said I unto you, that no man can come unto me, except it were given unto him of my Father.