The President is indeed the final word on the actions of our military during a time of declared war. During that time, the military does what he tells them. What the President tells the public and what he tells the military may be two different things, but that's up to him.
Does he have final power over the military during an undeclared conflict? That I don't know, but I do know that Vietnam, and in fact every US military conflict since WW2, has been an unofficially declared conflict. The word war is actually capitalized in our Constitution, leading me to believe that it is a proper term whose usage depends on the official procedures dictating its usage, and therefore any conflict the US engages in that is not declared as War cannot actually be referred to as war within the US.
It could be argued that any undeclared conflict entered into by the President and our military is a treasonous offense committed by the President. By entering into the conflict, they are effectively waging war against their own country by enticing the "enemy" to fight back, which is a reaction any reasonable person should expect in such a situation. In that respect, the President is both planning for and causing war to be waged against his own country.
So I just demonstrated how easily President Obama could possibly be charged with treason. To convict him it would only take either a direct confession by him, or the statements of two or more witnesses against him (there are a few more than that out there), and that would lead to the punishment for treason stated in the Constitution, which is death.
Did I just make a reasonable argument for sentencing our current president to the death penalty? I believe I did. Feel free to call me crazy, but you should back it up with your own reasonable argument stating otherwise, but keep in mind that you all now understand why the Founders included specific instructions in the Constitution on how to properly declare a war. Because when you don't, things tend to get messy.