Maybe you didn't get the memo. You gotta remember that the Constitution is a deeply flawed document because the Founders had a "blind spot" that prevented them from seeing "positive rights" (i.e. what the government MUST do for you), as opposed to "negative rights" (i.e. what the government can't do TO you).
Thus, it is our patriotic duty to correct the Founders' error, and break the constraints that are in the Constitution. This may be news to you, as it was to me, but hey, Obama himself has said so, and he's a Constitutional scholar!
Besides, it's a living document anyway, which means it has to be interpreted in light of modern sensibilities, not to mention foreign law.
So the way I see it, it means pretty much whatever anybody says it means. So if the troops don't like Obama, they can just tell him to go screw. That is, unless you're against the Constitution.
If the CIC disobeys the Constitution, the orders issued by said CIC become unlawful.