Such a military force would be facing a very well armed citizen-led guerilla response.
Given the amount of private gun ownership in the US, holding on to power after a coup would prove a rather difficult proposition.
As well-armed as the citizenry may be, the military is infinitely more so - they have, you know, tanks and planes and smart bombs - and in this fantasy civil war-esque scenario I don’t think the junta would be shy about exploiting that advantage.
Meanwhile improvised bombs seem to be far more important to and effective for a modern insurgency than firearms.
Add in that it sure seems to be more common to read about private militias aiding an authoritarian coup than successfully resisting it and I think the pro-widespread-individual-firearm-ownership faction has an uphill battle just to demonstrate that the practice is a wash, let alone beneficial to the preservation of liberty and democracy.
There are a few cases of private arms being used in anti-corruption "wars" or stand-offs in the US, but at least as many in which they're used for essentially the opposite purpose (supporting anti-liberty, and especially racist, policies and actions). In any case, the national guard stepping in tends to end these in a hurry.
The notion that the 2nd amendment is vital to the preservation of liberty and democracy in 2022 seems to be dubious at best. I'm not in favor of a blanket gun ban but I think that particular argument in favor of gun rights—which seems to be what anti-gun-regulation folks fall back on very quickly, when challenged, which makes sense as it's the reason given in founders' writings and, arguably, in the constitution—is, at best, pretty weak.
Unless enough citizens were on the side of the coup. I don't know why no one ever seems to acknowledge that as a possibility, especially after Jan. 6. Gun owners are just as driven by politics and ideology as anyone else.
Plus just because you have a gun in a safe and maybe sometimes shoot watermelons in the backyard with it doesn't mean you'll be effective in guerilla warfare against an actual military. I know Americans like to bring up Afghanistan and Vietnam as examples of guerilla warfare succeeding against the US, but fighters in both cases still went through training that would break the average American gun owner.
