Furthermore, there's no doubt that the U.S. can be at war without an official declaration by Congress: those instances when another country formally declares war on the U.S. first.
For example, the U.S. was officially at war with Japan from 7-8 December 1941, for a few hours with Germany and Italy on 11 December following their declaration of war against the U.S., and from 13 December 1941 to 6 June 1942 against Bulgaria.