Congress has not issued a declaration of war since World War II and the question of what kind of military action a president can or cannot take without one has been up in the air ever since.
The problem is that while Congress alone has authority to declare war, the president alone is the commander in chief of the armed forces.
After the U.S. got into protracted conflicts in Korea and Vietnam with no declaration of war, Congress tried to draw some boundaries when it passed the War Powers Resolution in 1973. It set requirements for Congressional notification and approval of any use of military force. But it passed over Richard Nixon's veto and no president since has ever acknowledged the law's constitutionality.
Still, a succession of presidents have sought Congressional authority for major military actions. President Bush 41, for instance, got Congressional approval for the first Gulf war and his son did the same for the Iraq and Afghanistan wars.
The best argument for doing so is not legal but political. Wars, even small and limited ones, can be politically corrosive and a President is on safer ground if Congress has approved. And such approval is a signal of unity to the enemy that can be militarily helpful.
So far, President Obama has not asked Congress to bless his Libya adventure, but he would be wise to do so, not least because it would bring his current actions more into line with his -- and his Vice President's -- previous pronouncements.