And the military leadership has been gutted so a coup is unlikely.
If you look at the history of military actions against civilian leadership, Many are not lead by generals, but by Colonels and even Majors. The lesson for any American leader planning extra-constitutional action is that controlling the generals is by no means enough. Indeed, our military is loyal to the Constitution above all, casting a great deal of doubt upon the ability of what amounts to a coup against the constitution to succeed.
Furthermore, do not forget that internally, state governors control a lot of military power. Under circumstances of any president attempting to stay in office and/or seize total power, how many National Guard Units (including Air Guard) would refuse to be federalized? Furthermore, state governments could raise militias relatively quickly and join together to oppose such extra-constitutional action. It should also not be assumed that only "red" states would join this effort.
The bottom line, IMHO, is that taking such action, without starting a civil war, is practically impossible. In fact, a civil war would likely be the best such a president could expect. A much more likely result of such an attempt would be the arrest of all supporters and a very quick impeachment.
Remember, we have had one civil war - and in that case the issues had taken a long time to develop and it was not about a president staying in power. In fact, the South never even tried to keep Buchanan in office past the end of his term. I really do not think that the US military would be willing to go to war against state forces (and likely US army and Marine units that defected to the side of states defending the Constitution) in order to keep an unpopular president in office past his term. I think the outcome is nearly a forgone conclusion. That is why I think it will never happen.