Congress has the sole power to decide when, where, against whom, and to what extent the United State will go war, according to this paper from Saikrishna Prakash: Unleashing the Dogs of War: What the Constitution Means by "Declare War". For the Founders, Prakash argues that there was more than the formal way to declare war that we typically think of today. Attacking an enemy was considered a declaration of war, so the Constitution leaves it solely to Congress to decide whether the nation goes to war. The President, as Commander-in-Chief, has standing constitutional authority to defend the property, territory and people of the United States, but he does not have inherent authority to take offensive actions without authorization from Congress.
The paper does a superb job of looking at what "declare war" meant in the 17th through early 19th centuries and why the "formalist" theory of the war power - that the President is free to wage war as he sees fit and that Congress' ability to declare war only changes the formal state of relations between two nations and triggers certain legislation at home - doesn't make any sense and falls under its own contradictions.
If we held to this construction of war powers today, much of the consternation this blog has expressed regarding the war power would be moot.