From a reader in response to the post below:

Jonah:
I have never thought about the Army being given an order to remove the president — as an American such is too horrible to imagine (which is why, my dislike for his politics notwithstanding, my sympathizes are on the side of the Honduran president).
The closest I could think in the US context may be the Indian removals during the time of Presidents Jackson and van Buren. The civilized tribes legally resisted the actions of the federal and Georgia governments to move them to Oklahoma. The Cherokee’s even won in the Supreme Court (it is probably apocryphal but Jackson is said to have exclaimed “Marshall made his ruling, let him enforce it”).
If ever there was a time for the army to refuse a US presidential order, it was that day.
But as to your question, the answer is probably no, the SCOTUS cannot tell the army what to do. But my (brief, two day old) understanding of Honduran constitutional law is that the army has a special status as protector of the constitution (they are the guardians of the elections for example) so the situation there is different.