The thing that comes to mind is that the military personnel take an oath to protect and defend the Constitution, not the president, congress, etc…
I imagine this doesn’t mean much to your average E-2 mechanic or infantryman, but as the officers get higher in the chain of command, they’re pretty serious about that kind of thing.
I think that the only situation that would cause the military to disobey the legitimate government would be one in which the “legitimate” government had lost its legitimacy by disregarding or abrogating the Constitution in some spectacular fashion.
A non-violent insurrection? I think that’s changing the meaning of the word.
Good examples of insurrections can now be seen in Syria and Iraq.
Isolated terror-style attacks do not rise to the level of an insurrection. Ordinarily, the insurrectionists control some of the national territory, in which law enforcement does side with the insurrection.
There’s another pattern where the insurrectionists control the night, and the incumbent government controls the day. But that seems unlikely in a country where the government forces have lots of night vision gear.
I’ve yet to see any evidence that these people are anything more than a handful of Tea Party conspiracy theorists. They are small fish in a very large and very crowded pond.