But to approach the topic with greater seriousness than Donald Trump ever could: throwing out the US Constitution and rewriting it from scratch might actually not be a bad idea. It is one of the oldest national constitutions still in existence, most other nations of equal or greater age have been through at least one complete rewrite in the meantime. Its language is antiquated; it uses a very old-fashioned amendment technique in which amendments are stuck on the end instead of modifying the main text in-place (which is what happens with most other national constitutions).
There is somewhat of consensus among political scientists that the presidential system used by the US and most of Latin America is inferior to the parliamentary system in terms of political stability. In fact, compared to Latin America, the US seems to have got rather lucky – avoiding many of the downsides of presidentialism in practice, in particular its tendency to produce caudillos – but is caudillo Trump a sign that America's luck is finally running out? Why not become a parliamentary republic, as in Ireland, Malta, Germany, Austria, Israel, Finland, etc? Prime Minister of the United States of America?
Of course, terminating the Constitution in that sense need not be done by a military coup – it could be done using the current amendment process, just with a mega-amendment to repeal and replace the whole thing. And maybe's that's all Trump meant. Or maybe Trump actually did mean a coup. Or maybe a bit of both. Or maybe even, Trump himself doesn't know what he meant, and doesn't care either.
Those prominent Americans include the original authors of said constitution: they always knew it would be a living document to be modified via amendments. Constitutional "originalists" who believe we should be totally beholden to a 240-year-old document with no changes are the ones who are not following either the spirit or the letter of the constitution.