If the army was there, fighting literally the rest of the US, would they engage in bloody street-to-street firefights? Nope. The easiest thing to do would just be level the damn place. The ENTIRE populace is hostile, so long as you don't send anyone in, everything there is a target. So you can just drop an MOAB in the middle of San Francisco without even the slightest fuck given. Sure, after the war you have to repair it all, but both sides in this hypothetical scenario are basically pulling a "No surrender!" thing.
America is a big place, and you can't MOAB every goddamn town in the whole US. The size is too much, the amount of people is too much. Only thing I could see is use of biological weaponry, and not even that really, there is too much empty space to hide in, and gas masks and other NBC equipment can be purchased without permit, and is a part of regular >surviving nuclear war prepper pack.
And what is there to stop something like that happening? Fuck. All. How many AA guns and SAM missiles are in civilian use? How many F-22s?
After they raid their closest supply depot, guarded by weekend soldiers, they gain access to heavy equipment.
Not only would the whole US populace be fighting a well armed foe, they'd be fighting a well armed foe with total air superiority.
Air bases can be captured too, and planes can be destroyed on ground. Sure, army got tanks, but simplest molotovs are deadly to superfluous turbine engine of Abrams, people would get their hands on IEDs, soon there would be self-made weaponry, which, with the technological and resource base, would be much more effective than the already very effective scrap weapons of middle east guerillas, and as I said, people would soon get into depots to get the weapons in store there.
Soon, US armed forces would be reduced to Navy, which is honestly only thing that can't be killed easily enough by infantry, but all that navy also need supplies. Sure, the nuclear carriers and submarines can just float around for years, but ultimately people on there need food and water, and it depends if some other country is willing to supply them.
In any case, US armed forces would be kicked out of their own country, and the civilians would soon form their own armed forces with heavy equipment and whatnot.