The military oath that I and every enlisted person and officer had to publicly state out loud reads:

"I, _____, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God."

There are historic reasons that "support and defend the Constitution" come before "obey the orders of the President." In basic training there was a class where it was explained that we have a duty to disobey unconstitutional orders. Likely because of My Lai massacre and the prosecution of Lt. Calley. I'm sure that officers get more extensive training in this area than enlisted people. I was just obeying orders is not a legitimate defense.