The Doctrine of Predestination presupposes that God put man into totaly Depravity so man would be unable to believe.
See Calvin's comments in Bk 3 on the reason Adam fell!
Your 'predestination' is simply God being arbitarary, creating most to send to Hell (for His glory) and saving some (no objective reason why any are chosen) to worship Him, thanking Him that they were not the ones sent to Hell.
Kind of like praising the arsonist for saving your life after he set the fire!
As for John 6:44, we also have John 12:32, that when Christ is raised up, He will draw all men to Him.
For further details see my posted article on 'Free grace vs forced grace'
http://www.freerepublic.com/focus/f-religion/940002/posts