The U.S. military's only oath is to the Constitution of the U.S., not the executive. They are to follow the orders of the executive to the point that they are in keeping with upholding the defense of the nation against all enemies, foreign and domestic.
Officers don't even take an oath to zealously follow orders, only to properly discharge the duties of their position.
While I'll grant that it's true that there is a lot of leeway and deference to the executive branch in what counts as a 'lawful order', it's incredibly concerning to me that so many people here have so little understanding of the U.S. military that they can claim with a straight face that the standing army is Obama's personal political tool.
Please see http://terminallance.com/2013/05/17/terminal-lance-president... for a description of how little reverence there is for the President within the military.