Presidents and the courts have used the Gulf of Tonkin Resolution and the Iraq Resolution as grounds to allow the sitting US President in his role as Commander In Chief to authorize the use of US forces in a police action against another sovereign nation. War need not be declared, nor was it in the case of Libya. Congress needs to authorize funding the action, but they can't technically stop the president from sending troops or warplanes somewhere.
And speaking for Canadians with similar political views to myself, we don't have a problem with war per se. We disagree with how the Afghan War has been executed (massive corruption and war profiteering hav not helped win their hearts and minds) and we disagree with the Iraq War both for the equally corrupt way the occupation has been run and for the fact that it was a war of aggression waged on manufactured intelligence. It's not quite as simple as "hurr, war bad, durr hurr".