I think, to post a garrison in each town with 10,000 people or more, the government would have to call a lot of our soldiers home from overseas. I doubt the government would be willing to do that. Otherwise, they'd have to draft more soldiers and the liberal soccer moms aren't going to like having their babies drafted. Remember, pissed off soccer moms have a loud political voice.
Either way, taking in a couple of the soldiers could work to our advantage. Make friends with them, treat them good, treat them like family, they'd be less likely to shoot you if you refused to give up your guns. If enough of the soldiers are sympathetic to the people of the town, you could almost have a government trained, and supplied, militia helping to protect your rights.
I realize that this is an overly optimistic idea, but it's hard for me to believe that most Americans are like the people we've been hearing about from NOLA.