Could the U.S. Supreme Court Order the Military to Arrest President Obama?

Or put in the name of another person as President. A sort of question related to my post Did the Obama Adminstration and the World Jump the Gun On Honduras ? See this timeline here

The major legal blog The Volokh Conspiracy has that as their question of the day.

If a nation's military, acting under the orders of its Supreme Court, moves to arrest the president of the country for openly violating its constitution in ways that will promote his own power, is that accurately described as a "coup?"

The comments are interesting. Now of course the Constitutions are different. But what if Congress could not convene in time for impeachment proceedings and it was a time of much peril because the President was going to do x that was a threat to the Republic and was so in the face of the Const. Would the Court find it in it's inherent powers to act? Could it? Would it be a Coup?

This is the Oath that Supreme Court Justices take

"I, [NAME], do solemnly swear (or affirm) that I will administer justice without respect to persons, and do equal right to the poor and to the rich, and that I will faithfully and impartially discharge and perform all the duties incumbent upon me as [TITLE] under the Constitution and laws of the United States. So help me God."

Here is the oath of the Armed Forces

I , (NAME), 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.

In the National Guard (Army or Air)

(NAME), do solemnly swear (or affirm) that I will support and defend the Constitution of the United States and the State of (STATE NAME) 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 Governor of (STATE NAME) and the orders of the officers appointed over me, according to law and regulations. So help me God.

Thankfully I never think we will be in this situation Or so we hope.