I'd say my chances are pretty good, barring some major biological or nuclear fallout situation.
The chances of SD being ground zero for anything like this would be pretty slim and it would probably take a few/several weeks to work itself in this far.
I'm armed to the teeth... so could hold my ground for some time, but food would get scarce within a month or two based on what I have on hand now. My water situation is probably worse, but the river isn't far. I don't have more than 10 gal of gasoline at any one time (excepting what's in the the vehicles at the time), so that could lead to some interesting obstacles.
Of course, if it was in the middle of winter... that would complicate things greatly.