What does he mean by quoting that verse? Does he think it says that at the time of Christ's 1st coming, no one had (yet) been received into heaven?
Since that's not the point of Jesus' statement, it seems completely irrelevant to the discussion to drop it in the way he has. Jesus' words aren't an absolute statement that no man has been brought to heaven.
Jesus' statement sounds like an allusion to Dt.30:12. Paul makes reference to the same text in Rom.10:6. In both places, the sufficiency of the Word is in view, the difference being that Paul's exposition focuses on the Word preached, while Jesus is making a self-referential comment.
Men cannot attain to God (ascend to heaven) on their own, but God has made the way to himself through his Mediator, who has come down. And he comes, that men might have a home in heaven.
Some readers of Scripture can't see how the virtue of Christ's sacrifice can be applied to OT figures prior to the historical event of Christ's cross. Apparently, in this view: faith and hope in Christ-to-come isn't existentially saving for such believers; rather, the foreordination of Christ to this work is insufficient for the application of its benefits--perhaps there's still a big "uncertainty" (for God?) until the sacrifice is made in history.
I would guess there might be problems among those you're conversing with, over the matter of meticulous predestination as well. Even if they believe that God "gets his will done" at times by sheer force, it sounds like they could be wedded to a realist notion: that until something has come to be historically, it has no existential weight or substance. In that case, since heaven demands the sacrifice of Christ, until it happens historically, the gates are barred historically. (Also implies that men's souls are entirely historically and otherwise bound by the laws of this life.)