I'm inclined to say they can declare war against the President's will, but the President as Commander-in-Chief, can simply refuse to deploy troops or do any action that would constitute an act of war.
this is true. Of course if ~80% of the country is for action along with Congress, the military might just go at it anyway while the politicos do a "soft coup" at home. For example, say Putin starts dropping tactical nukes and we sit on our hands. Then he invades Estonia, and we sit on our hands. Then he nukes Warsaw, and everyone is like, "whoa, we have to do something now", Congress declares war and the sitting POTUS says "nah". We've got us a problem at that point.
