The United States Military and the Oath of Enlistment

The military Oath of Enlistment says “… that I will support and defend the Constitution of the United States against all enemies, foreign and domestic …” (underline is ours) and it also says “… that I will obey the orders of the President of the United States ….” So what happens when these requirements are in conflict? All military personnel know that they can refuse to follow a direct order if they deem that order to be illegal or improper…