I got lawyers guns and money. Handle this x)
I've actually got half a notebook of musings on this very subject. The way I imagine it, marines and army would most likely form "outposts" of sorts. Shotwave communications linking them incredibly loosely, divided by geography and former population density. The fleet (i'm in the Navy) would get much leaner. Probably eliminate females from the service altogether. No BS tolerated - endanger the mission = walk the plank kinda discipline. Probably have zero use for the sub fleet, or nuclear carriers. Easier to raid fossil fuel supplies that are laying dormant and train surivivors on diesel engines than it would be to train nuclear engineers. So we'd switch to 4~ diesel dependency and have to take what we needed.
I envision the center of whatever government there is being based on islands. The the "forward outposts" being places such as Coronado in San Diego. Easier to take an island than an inland mass. then fortify it. clean-sweep of the perimeter daily with soundless weapons. From there, loose coordination with whatever joint service outposts existed could be coordinated. But honestly, overall, I imagine we do only marginally better than the better organized civilian factions. But yes, a little better.
"You don't gotta believe in your government to be a good citizen.. You just gotta believe in your country."