That power was ruled unconstitutional by the Supreme Court and overturned.
I don't recall anyone paying any kind of price for that even though it was a complete abdication of Congress' authority.
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...
I think it's every citizen's right - even duty - to be questioning these things rather than leaving it to some "Constitutional expert".
I'd encourage the original poster to drop the loaded term "ObamaCare" and instead explain why he believes the health care bill is not allowed under the interstate commerce clause. In my opinion, it isn't a very difficult thing to argue.
Every American has the right to question whether or not a law is constitutional. However, without expertise in constitutional law and elections, it is speculative to make claims that senators were ousted because voters believed a law to be unconstitutional.