Even if our military gave up we have enough civilians who know how to use a gun to daunt the armed forces of most single African Nations. And besides, if the military just gave up the hardware would still be around: tanks. planes, bombs and such. And all aside we have pretty kickass units in our law agencies that rival the special forces of most countries. And if we had to we would mount an insurgency that would make the IRA's campaign look like a bunch of drunk brawls.
I mean, you think what were doing to the Taliban and Al-Quade is all out? We are concerned with conserving resources, not winning. Those guys only blew up a few buildings, try landing troops on our shore (if you could get passed our Coast Gaurd and Navy) and we will tear apart the world to get you. We will go all out with everything, and thats not counting our WMD's.
The point is that unless the Union dissolved there would be no profit to attacking the U.S., because in order to neutralize our capability to resist you would have to blow up half our country, if we dont do it first so you dont get your hands on it. By the time you win all you would have is a smoking wasteland, burned out cities and guess what - no resources worth even fighting for. Not oil, diamonds or anything that has intrensic value because we here are all about credit.