Skeptic Project

No.

The President can commit troops (or planes, or whatever) wherever he likes. Under the War Powers Act of 1973, once he does commit troops, he has 30 days to "report" to Congress. Historically this "report" has been a formality, a 1-page bullshit document. Obama will certainly file it in this case, probably after whatever's happening in Libya is already over, but its only legal effect will be to comply with the War Powers Act.

The President cannot declare war, but that's also a formality, considering it hasn't been done since 1941. Historical practice, and certainly political reality, has made formal Congressional declaration of war a thing of the past. I doubt it will ever happen again, though I was almost alone in arguing that Bush should have asked Congress for a declaration of war on Afghanistan, Al-Qaeda and Osama bin Laden in September 2001. (There's nothing that says you have to declare war on another sovereign state. I believe the U.S. could have declared war on Osama bin Laden personally, or on Al-Qaeda as a non-state actor, with exactly the same legal force).

Constitutionally the only way Congress could stop action against Libya would be by passing a resolution formally withdrawing funding for that operation, but even then it couldn't become law unless Obama signed it. Since he would surely veto, and there aren't enough Republican votes to override his veto, Obama would still win. In any event it would never happen because any vote to suspend funding for military action already in progress is a political non-starter, leading immediately to "you don't support our troops!" claims. Throughout the entirety of the Democratic control of Congress, for instance, 2006-10, they never did withdraw funding for Iraq even though most Democrats were against it.