From what I understand, the process wouldn't be for Congress to decide whether it liked the recisions. The process would be for Congress to decide whether the bill, with recisions, was better than no bill at all. If Congress wanted to have fewer recisions, it could attempt to introduce a new version of the bill, with some of the recisions but not all; this would then put the ball back into the President's court as to whether to accept it, making clear that if he rejected it the result would probably be no bill at all.
Ah, I see, so it's really not much of a line item veto the way I think of it, then. Which I guess is necessary to avoid running head on into the precedent set on the previous try. Ah well, it might be an interesting executive power, but I don't see it being that valuable.