I think you are confusing the President's war making powers under Article 2 with the President's law enforcement powers. Listening in on enemy communications has nothing to do with law enforcement. Signals intelligence is what we did when we broke the Japanese code and learned of their plans to invade Midway Island in World War II.
Think of it this way, if FDR was listening in on conversations between the German High Command and Nazi spies in the U.S., would he have had to have a warrant first? Of course not. The warrant requirement under the Fourth Amendment only applies to unreasonable searches and seizures, which has been interpreted to mean searches and seizures conducted as part of law enforcement. The courts have never considered Signals Intelligence to be an unreasonable search and seizure.
It depends on where that signals intelligence is gathered. If abroad, then fine. If during the course of signals intelligence gathered abroad a domestic phone number, etc., arises, then a warrant can be secured to pursue that lead. By way of contrast, domestic signals intelligence would be flatly unconstitutional sans a warrant - a warrant is required for domestic law enforcement purposes; the president has no domestic warmaking powers in the absence of civil war, revolution, insurrection, or the like.
In other words, if conducted domestically, signals intelligence becomes, on the face of it, a law enforcement issue that must pass constitutional muster. If the courts have decided otherwise, then they have decided poorly. Nothing remarkable about that as the Kelo and CFR decisions among others in recent years have amply demonstrated.
It goes without saying that I do not concur with your assessment that the post 9-11 congressional resolution is a declaration of war. Rather, it is a prescription for permanent government employment of emergency powers because war against an unidentified and undefined enemy, against a tactic rather than countries and people known to promote, foster, and practice it, is inherently unwinnable.