Immediate removal of this President by the US military, followed by a trial for treason and new elections.
Which, of course, would amount to abrogation of the current Constitution. So he will get his wish in the end 
Not necessarily. Congress could rush through an impeachment, or even if the military deposed him and had the VP (or House Speaker) take over, it wouldn't mean the abolishment of the Constitution. Lawmakers have passed laws they know are unconstitutional just to have them ruled that way later on, and cops have acted in unconstitutional manners as well. Their removal of him would just be a violation and then hopefully, back to business as usual.
There is a big difference between impeachment and removal (which is competely legitimate) and a military takeover. A military takeover is far outside of the US constitutional system. Any general that does it would not be able to easily restore the constitutional order, because, once it is restored, he would, almost certainly, be prosecuted for treason himself. In fact, failing to prosecute would open the doors for the military to effectively become the top court, determining legality of executive action: something that is so far outside the US constitutional system, that this by itself would result in effective abrogation of the present Constitution. The military that, whatever the circumstances, takes the lead here, is in rebellion, and that rebellion would have to be suppressed before the constitutional order is restored. But, of course, that means that the leader of such a military junta would be loathe to give up power - since power would be the only thing keeping him out of jail. So, chances are, if such an incredible thing were to happen, it would be followed by a few years of a military dictatorship.
Again, the issue is not that the president cannot be impeached and removed: of course s/he can. But an impeachment does not require any serious action on the part of the military (all the military has to do is to follow the orders of whoever becomes president according to the line of succession after the president is removed by the Senate). Any course of events in which the behavior of the military becomes news, is tantamount to the most radical change in US constitution order imaginable.
