If it’s not a war, but something short of war, then the President has the authority to commit forces as Commander-in-Chief. In the past, it’s worked for us, such as Grenada; we can’t start playing Democrat and changing our minds for political convenience when it works against us.
Similar situation, but different enough.
Grenada was facing a commie takeover, sponsored by Cuber and of course slightly, sort of directly by the Soviet Union. Another Cuba, this time in the southern Caribbean was not in our interests.
Grenada is not exactly in our backyard but certainly just over the fence. Monroe doctrine anyone?
As opposed to Grenada, the political affiliation of the tyrant of Libya is irrelevant to us.