It really depends on how we adapt to the aftermath.
Bear in mind that we’d be paying all the soldiers, sailors, marines, and government employees either way, whether through wages, salary, or unemployment. But we’d still save a fuckton of money as payroll is not the only thing our military dollars go towards.
And we aren’t exactly at great risk of invasion either; global warming pretty much keeps the Bering Strait from freezing solid enough to march troops over. Even if they did, I’m pretty sure Kim’s soldiers wouldn’t last too long in South Central (outgunned), and there’s plenty of NRA members that’d be happy to do a little “charity work” anyways.
Yes, there would be an initial shock as certain towns get their financial core ripped out… unless we somehow replace it with something else. Many towns only exist because of mining even today, and if we wanted to take some of the money we saved and put it towards repairing/upgrading our infrastructure to late-20th-century standards, we’d be retooling a lot of plants to make a different type of product and placing enough orders to give our manufacturing sector a shot of steroids; machinists don’t care if they’re making a wing spar for a fighter jet or a steering knuckle for a dump truck so long as they get paid.
That said, removing the social safety net would likely lose any immediate savings due to the increased need for police (possibly even National Guard) and would have other ripple effects as well. I know that if someone’s car got stolen and taken to a chop shop so that someone else could buy groceries, they’re probably going to miss a few days from work.. and I likely wouldn’t be the only one. And that assumes that I even feel safe leaving the house instead of staying home to protect my stuff from looters. Lost productivity plus increased Law Enforcement costs equals savings?
Honestly, there are too many variables to really say for sure.