Congress raises and supports the military, but the president is the commander. Declaring war and making war are two different functions. There's no question President Obama has the authority to do what he did (via First Read):
“Mr. Obama's actions are consistent with the way every president since Richard Nixon has treated the War Powers Act, choosing to notify Congress only after a decision has been made to sign orders authorizing military operations.”
A point to consider…
“His actions do, however, appear to contradict the view he expressed as a candidate. In December 2007, he told Charlie Savage, then of the Boston Globe that a president "does not have power under the Constitution to unilaterally authorize a military attack in a situation that does not involve stopping an actual or imminent threat to the nation."
“So who's right? Constitutional questions, and legal battles over violations of federal laws, are normally resolved by judges. But this is an area where the courts have been reluctant to tread, unwilling to referee what they see as disputes between the political branches of the government.”
So where does that leave us?