Good point. And actually, I may not be particularly well liked for this, but a line item veto is an awful idea. Should we really give presidents the ability to punish political opponents by removing all their projects? Just because we're against pork doesn't mean the president, rather than Congress, should have the right to pick and choose what pork to keep and what pork to cut. I'd hate to imagine the Clintons with the line item veto...
I'm not a fan of it either. I first proposed twenty years ago to give the Vice-President and the Speaker the power to divide bills into pieces for a separate vote. Call it a "cedo" meaning, "I cut," as in dividing it with a sword.
As far as I can tell, setting up the cedo would not require more than a rule change.
I like your thinking on this issue.