War and hostilities are not quite the same thing. Consider the so called "sitskrieg" at the begining stages of WW-II for example. The President, acting as commander in chief, can decide wether and when to inititate hositle/military action. Just because he chooses not to do so at any partiuclar time, or ever, does not change the fact that a state of war exists. Jefferson could decide whether and/or when to use military force against the pirates, but in any event, he was authorized by Congress to use that force. He wasn't directed to use it, and in fact I don't directing him do so would be Constitutional, as it would usurp his powers as Commander in Chief.
Now all this aside, I'd like a Declaration of War, for a number of reasons, not the least of which would be to make absolutely clear that the actions of those supporting Saddam do indeed constitute Treason, although I don't believe a DoW is require for that, but it would make it clear. However that's not going to happen for a number of reasons, both domestic and diplomatic, mores the pity. At least we have the Congress and the President more or less on the same page, which is what the split powers of Declaring War and of the commander in Chief, was all about.
Except a declaration of war does exactly that. By placing the nation in a state of war, Congress obliges the President to prosecute it. The situation is exactly analogous to when Congress passes a law. The executive is obliged to enforce it. In both cases, it is the job of the executive to execute policy, not initiate it.