RE: The oath is not only to the Constitution, it is to obey the lawful orders of the officers assigned over you and the POTUS
Officers swear an oath to protect and defend the Constitution of the United States and not to POTUS. In Nazi Germany the military swore an oath to Hitler and not to Germany
The oath is to protect and defend the Constitution and to OBEY the LAWFUL orders of the PRESIDENT of these United States. While the first part of the oath is to protect and defend the Constitution in principle; the second part of the oath is to OBEY lawful orders in practice.
While the oath is not sworn TO either the Constitution or the Presidency (it is sworn to God), it obligates one to obey the lawful orders of the President.