Wrong. Congress authorized him to act under the UN Charter and under the NATO treaty complex.
He is exercising the deployment authorization that Congress, through those treaties, gave him.
If they didn't want him to use the treaties, they shouldn't have passed them. If they don't want him to use the forces, they should defund the DOD.
Until then, they are just engaging in an unconstitutional power grab.
Our treaty obligations under NATO (let alone the UN Charter) do not remove the power of Congress under the Constitution to declare war.
Congress need not defund the entire DOD either, they can decide that no U.S. money will go to funding any military missions in Libya or to NATO or to the UN or to any other cause that they feel doesn't deserve taxpayer money.
http://www.nato.int/cps/en/natolive/official_texts_17120.htm
Was a NATO member attacked? And even if attacked - the treaty obligates us to treat an attack on a member state as if it were an attack upon ourselves.
An attack on the USA, like the one at Pearl Harbor, did not remove the power and obligation of Congress to declare war. Neither would a similar type of attack on England that must, under NATO obligations, be treated as an attack on the USA.
It isn't really that difficult a concept.