One problem with that scenario.....if the SHTF, beyond the early days, most of the trucking industry will stop, which means much needed supplies like fuel don't get delivered. Unless, this military faction has deep supply lines and the ability to defend them.
The problem with this is that the US is a rather large area and it would be difficult to conduct operations very far away from things like refineries. Eventually, your tanks, APCs, and IFVs would become little more than stationary cannons.
Sure, you could do things like wars past, and walk/pack mule everywhere you go and hump your mortar systems, machine guns, and rocket launchers. Unfortunately for them, any formidable force would probably be spotted in small rural communities. I would also imagine that large numbers of the military/NG would desert in order to be with their families (after looting the armories and ASPs of course).
You currently have a large force of service members/veterans that have experience conducting COIN. This means that you have large numbers of people that understand the basic concepts behind things like IEDs, as well as, more advanced concepts like improvised rocket launchers, pressure plate initiators, and explosively formed penetrators. A whole lot of havoc could be wreaked by a relatively few individuals.
Sure, I would agree that large military supply depots and things like the strategic oil reserve could keep a large military force going for awhile. But if you start talking about a large breakdown in overall law and order, it won't be long until some of those same militants loot the larger force's supplies for personal gain, or just sabotage it; these guys do have families that don't live near the base. It doesn't take a lot of imagination to figure out this force can be used to violently destroy the area you grew up.
If law and order wasn't established within the first few months to a year, I could foresee insurgent forces long before large military factions.....at least until someone manages to co-op several smaller forces and provide some semblance of law and order. Especially since there are so many competing interests. I'm picturing something along the lines of Somali warlords, and tribal/insurgent forces similar to Iraq and Afghanistan.
One of the reasons America is as large as it is, is because of the ties that bound us. There is a reason, the US doesn't encompass all of Canada and South America. After the shooting starts, how much similarity is there between say Dallas, TX and Manhattan, NY? How difficult will it be, during civil war, to raise a force that aligns California with Kentucky? Againg, you are looking at various warlords, vice large standing armies squaring off like in WWII.
The factor you mention is neither new, nor something left unaddressed by military people who have been contemplating what would be necessary for a successful counterinsurgency since the Eisenhower presidency.
Fuel is a insurmountable problem in some parts of the world, but not here.
This all reminds me of an old board game called “After the Holocaust”.
ATH was a scenario of a post-nuclear exchange in America, the huge die-off that followed, and how society began recovering over a 20-year period.
The recovery coalesced around regional entities that were more by random chance than natural selection. In the Northeast, it was AT&T. In the Southwest, a mix of state police, National Guard, and veterans associations. In the West Coast, Bank of America. In the Midwest, the “Church of the Chosen Few”, a splinter of the Missouri Synod.
Each group had a memory of a UNITED States of America, and was convinced that their memory was better than the others.
This is not a minor point.
A bit less than a decade ago when I was working for a newspaper in the southwest United States, I was reporting on a man who took over someone else’s house, barricaded himself by pretty much wrecking the contents of the house, and tried to provoke an armed standoff with police. I do not remember all the details at this point other than that the police waited him out and the man eventually killed himself.
However, before killing himself, the man set lots of traps in the house to kill or severely injure anyone who entered the house to get him. Those traps had to be disarmed. It was a huge mess, to put it mildly.
The relevant point is that I made the mistake in my article of calling the items in the house “improvised explosive devices.” That was technically true since he had created homemade bombs with a variety of trigger mechanisms, but calling them “improvised explosive devices” rather than “homemade bombs” wrongly implied a connection with the stuff going on in Iraq and Afghanistan at the time. I wouldn't make that mistake today, but back then the phrase was still being used in civilian circles without the connotation it now carries after a decade of dealing with Iraq and Afghanistan.
Let's just say military personnel picked up on my article and the local police had to field lots of questions about whether the technology to manufacture Iraq-style IEDs had migrated from the Middle East over to an American criminal environment. Fortunately for everyone, the problem was a dumb reporter (me) using a poor choice of words, not that gangs and individual renegades had acquired the ability to use IEDs in an American environment.
Our troops dealing with IEDs spend most of their time training to detect and disarm them, not create them. Bombmaking is a skill and it's not necessarily easy. However, in a real SHTF scenario, we can assume that just as happened with leftover or cast-off military munitions in previous wars, the technology to make IEDs will start being used by local non-military forces, sometimes for defensive purposes to protect property, but unfortunately sometimes for very different purposes.