Sadly, you are more right than not.
The oath of enlistment is to the Constitution, not the President, not the Congress, and not the USSC... in fact any of those could, conceivably become the domestic enemies which they are to defend the Constitution against.
Officially: To have legitimacy, a General or two would have to authorize the move against the government, but I doubt that would happen because, as Col. Hackworth said “They’re a bunch of perfumed princes”... IOW, they are themselves enmeshed in the politics of corruption they should be standing against.
Unofficially: I think there may be some unrest in the ranks. Right is right and wrong is wrong; everyone knows this, even if they adamantly deny it. If a non-trivial portion of the enlisted “broke ranks” and marched on DC, things would get VERY interesting VERY quick... you can bet on it.
The people who cheered when G.W. Bush mangled parts of the Constitution in the name of fighting terror now find those precedents being used and built upon to amass ever greater power to the fraud in the White House and his co-conspirators.
It would take some type of general indeed to decide that the enemies to the Constitution were domestic, and that only a military solution could save it.
And how would he start? One wrong step, one failed attempt at recruiting a core of senior officers, and that would be it. Running across one general staffer who thinks, “Hmm, if I go along with general DBrow, I may not get another star. But if I turn him in, I definitely will, before I retire”. Then, he’d have to get a bunch of light colonels too, and a gaggle of lower officers, and a division or two of enlisted before he could move.
As for the “enlisted” scenario, let us pray that we don’t descend into that type of chaos.
Keep in mind... Qaddafi was a colonel. Most coups are led by colonels who don't really care for perfumed princes... I don't give a hoot who in the military takes the initiative. He/she has my support! The commander of the Alaska National Guard works especially well for me!