The 45th president, on Day 1, announces a New Constitution. The Reaction?

[Virginiá]

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.

[Virginiá]

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.

I suppose. It would be a unique and difficult event, but I truly think that it is more likely the military would remove him from office and return control to whoever is next in line. It doesn't have to invalidate the Constitution (or even part of it). The rule of law and order in this country is far more stable and respected than most countries vulnerable to this type of takeover. Plus, I like to think that the military leaders would understand that trying to stay in power would almost surely result in a civil war and that they wouldn't be able to depend on continued control of the military in such an event.

Though, none of this is to say it couldn't happen, but rather that I think it is more likely than not to return to regular order after a short spell of disorder. Probably would also be fair to say that whichever political party the rogue president came from would be done for.

[Virginiá]

But what if at least 34 senators and the Joint Chiefs of Staff back the president's plan?  No one has yet considered this possibility.  The senate would fail to convict and the president would remain in office.  Post-1945, any serious civil war would be decisively won by the federal government within hours.  For the states, it would be either appoint delegates to the constitutional convention or hope the federal government lets you secede peacefully, at the risk of having your largest cities destroyed and then being subject to Reconstruction 2.0.  If military defectors somehow got nuclear weapons to the rebelling states, I suppose there could be a prolonged cold war scenario between the states.  Scary scenarios all around!

Sounds like the show "Jericho" (namely Season 2)