Not even remotely to the level of what we currently see in America.
Does it really matter? It's all relative.
First off, lets just take nukes off the table, they're irrelevant, no American despotic President's going to drop nukes on Los Angeles or whatever to quash a rebellion. It's so outside the realm of possibility it might as well not be considered.
So what now?
The Navy's not going to be doing much unless the French decide to help us out again which would be unlikely. I don't exactly envision a scenario where unleashing the full might of the US military on the civilian population makes sense but unleashing it on a foreign power would have much less consequences domestically. So I don't see anyone officially aiding us in this scenario.
Now we're really left just dealing with the Air Force, Marines and Army. A much fairer fight, though still technically one sided. I don't really see the US military's SOP for insurgencies working here on our own soil. You're not likely to see a return of carpet bombing like the Vietnamese war unless everyone decides to gather in some desolate forest or some shit. The idea of some American insurgents running into the Empire State Building or something just to get a laser guided bomb dropped on them is ludicrous. I mean, it could happen but how long could a regime like that stay in power here, really? So we're not likely to hold any cities outright or field any armor but whatever, if the people were dedicated they wouldn't need them.
So then the main threat will come from the Army and the Marines and boy would that be messy. We don't exactly have a Northern Alliance or any tribes we can ally with so they'd have to quash this rebellion with their own hands. I'm not saying this couldn't happen I just don't think it could be sustained. Think about what a war like this would devolve into. For the most part a good portion of our military men and women live among us. Their kids go to school with your kids. They get their hair cut in the same places you do. Go to movies the same places you do. You'd have servicemen and women getting killed in town, places they frequent getting bombed, kids spitting on their kids at school for actions their parents or others in uniform are committing in the country. Only a matter of time until they themselves break or all servicemen, women and their families have to live on base when not on deployment due to not being able to be out in public anymore. Either of those have severe consequences, bases don't have the resources to house and school all their personnel and families and even if they built them what a mental toll that must be to not be able to walk around in your own country. Or maybe they'd have to start deploying soldiers from overseas whose families would be safer in Korea, Italy or Germany than the units stationed here at home. But it'd be a fucking shit show that's for sure.
But they're not safe on base either. Many bases are large sprawling bases next to somewhat large civilian communities. Security's based on the idea that you're somewhat safe in your own country so it's not like there's fucking roving APCs and tanks everywhere. Having to actually actively defend large bases like Fort Benning and the like would be a drain on resources.
In the end I can't really say specifically what'd happen or how vulnerable troops would be until we saw how they decided to fight it. If they decided to fight it 100% and essentially deployed everyone base security's kinda less important if all the units are out in the country oppressing people, doing martial law or blowing up cities, whatever they're doing in this scenario. But depending on how paranoid or business as usual they try and play it they'd be varying levels of vulnerable from base to their final deployment. In the towns and cities they'd be walking ducks for insurgents to pick off and their families would be fair game. Many of their supplies and equipment might be transported via rail which would leave them vulnerable to theft or sabotage. And any mistakes would likely just add fuel to the fire. Not like Americans particularly like civilian casualties even if they do tolerate them overseas but blowing up American homes and businesses to get a few terrorists or revolutionaries is going to turn people against you pretty quick. We don't exactly have a good track record of winning those types of battles either but perhaps this hypothetical despot would fight harder since it's his/her own power on the line here.
But then, what exactly has happened to our government? Are they playing it cool or is it a blatant military take over? Because if they're trying to present themselves as the real continuation of the US government while simultaneously bombing civilians and revolutionaries alike in our own cities they'd kinda have to keep up the pretense a little, right? So now you also have to think about securing all our politicians and our President. He's only really safe in the White House now because you're worrying about a lone wolf or two trying to kill the President not a fucking insurgency. The Secret Service couldn't hold out if a tenth of Washington DC decided they were going to try and kill the President. So is this despot President and all government officials going to hide in a bunker the whole time? If so, I have a hard time imagining that going over well with the American people too and that just adding to the fire if all of a sudden government just up and goes into hiding, no longer doing town halls, no facing the voters, no Press Secretary answering questions, yikes. I assume this despot would also want to extend their term, right? I mean, surely killing a ton of Americans would open you up to reprisal once you left office, I'm sure that'd go swimmingly.
I just can't actually see a way a revolution doesn't work in this country provided it's a proper revolution that a large part of the population agrees with.
Edit: Put simply I feel like if the US actually needed to use its' military's might it's already lost and if your revolution doesn't warrant a military response you've already lost.
