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.
Remove the part where it's easy to get things Stateside, and I assure you, a U.S. military coup/junta will be fighting a two sided war as well. Both internal from the populace, and external from former Allies who in no way, shape, or form are going to sit idly by and be threatened by a militaristic U.S. Armed Forces that's even remotely controversial enough to even be considered a coup by the populace.
People forget: The Army Sabotage Manual is public domain.
The military knows exactly the hell it will be entrenched in if it ever goes against the public's wishes. They literally wrote the book.
The US military problem would be that it has to subdue a population that has been socialized to resist (to the point that it already birthed paramilitary during the previous democracy) and constitutes the replacements for that military (and the industries necessary for supply) for coming generations. Hell, once it had a democracy the first time, it still went to civil war. Thinking about the short term doesn't get you much.
Predator drones, nukes, etc won't solve the problems that couldnt be solved in a foreign land. Domestically it would be harder and longer fought.
For example, let's say that the military made a deal with <insert the most extreme sub-faction of your least favorite party here>. Then they'd have people to install into the newly vacated positions of civilian economic administration, and in that, they'd have a way to motivate that faction to join them and support their legitimacy.
The entire public’s wishes, yes. Now consider what would have happened if the military leadership hadn’t resisted the call to join the January 6th insurrection — it’s much easier to imagine something like 90s Serbia where a substantial fraction of the population hopped up on propaganda supports the military efforts and will keep their neighbors from forming an effective resistance.