Article I, Section 8 gives Congress the power to "declare War . . .", but nowhere does it say that the president can't, nor does it say that the Congress has the sole authority.
On a more serious note, the question of "war" is not black-and-white. Is our policing of the no-fly zone "war?" Why or why not? Can hostilities be initiated without a declaration of war? How long can military action be maintained without a declaration of war? See Korea and Viet Nam. Also, nowhere does it say that a Congressional declaration, should one be forthcoming, be unanimous. Many well-reasoned people were opposed to the Revolutionary War (they were wrong-headed, IMO, but that is another discussion)