In trying to answer a question about what the president does, I'm currently hung up on "war".
See: https://politics.stackexchange.com/a/11878/8298 for more details.
Essentially, my statement is that the President can not start a war. That he can only respond to war declaration by congress. He can certainly support a war politically but the act of declaring a war is outside his "powers".
The counter to this argument is that while technically accurate the US no longer declares war in that manor, and thus it's a misleading point.
Which leads me to the interesting question; Has the US president ever "gone to war" that the legislative branch did not support?
Now for this question, war should mean military action, and should not include instances of the US participating in UN military actions where we were obligated to do so because of a treaty ratified by congress, but could include the president doing an end around and going to UN route to force the point.
Also as far as "support" is concerned, I don't mean popular support, I mean a resolution, act, bill, or some such that granted powers to the president.
Clandestine operations don't count either, as they fall under a whole different ball of wax.