No, Andrew, We Aren't

"At war," that is, assuming that Andrew Sullivan means the government of the United States (a reasonably safe assumption, since the topic under discussion is the limits of executive power within that system of government).

The US Constitution delegates the power to declare war to Congress. Congress hasn't exercised that power since 1941.

No, the "authorizations to use force" passed by Congress after 9/11 were not declarations of war. They included "war powers reservations" to make it clear that they weren't declarations of war, and Congress overwhelmingly voted down resolutions declaring war on e.g. Afghanistan and Iraq.

If you want to argue that the US is in a state of de facto war, or that the current situation is morally equivalent to war, knock yourself out. That's irrelevant to what powers the executive branch possesses in time of war, because that's a legal matter -- until and unless Congress has declared war, the US is not, in any legal sense (the Constitution being "the Supreme Law of the Land"), at war. Period.