So, it's daft to try to reinvent an outdated concept. They're just a bunch of Bush-haters creating a system they hope would have thwarted him from going into Iraq. But Congress was asked to vote on that and said yes. Oh, never mind!
I think having Congress authorize the President to wage war meets the requirements of the Constitution--it is the functional equivalent of a Congressional declaration of war. The only difference is that we are not actually at war when the resolution passes; we are just authorizing the President to initiate it at a later time if he so chooses. In essence, Congress has delegated the actual initiation of war to the President, for that particular conflict. There's no formal "declaration", but when the President acts following Congressional authorization, a. war exists; and b. Congress approved it.
One corollary would be that if Congress rescinds an authorization BEFORE war has begun, then the President no longer is authorized to act. Once war has begun, however, the President as commander in chief is responsible for fighting it, and cannot be made to stop. Congress' role is to fund or defund it, and to approve any treaty that results.