That's a somewhat inaccurate summary. Reagan had also explicitly asked for it, and the 1996 bill was introduced and mostly supported by the Republicans, who you may recall had a Congressional majority at the time. Senator Bob Dole, who introduced the bill, was the GOP candidate for president in the same year, and one has to wonder if its introduction was partially aimed at burnishing his credentials as an opponent of pork-barrel politics. There were two attempts to bring it back in 2006, both sponsored by prominent Republicans.

Any president would like more authority over the budget, but the GOP does seem to have invested the most political capital in it. The general public seems fairly indifferent to the niceties of constitutional law so I'm not surprised the proponents haven't suffered any major electoral rebukes.

http://en.wikipedia.org/wiki/Line-item_veto_in_the_United_St...

http://www.senate.gov/legislative/LIS/roll_call_lists/roll_c...