Sure our paper money is worth something now because our government and our military say so. As just one example, a Tunguska event over Washington instead of Siberia would have wiped out the value of our paper money. That's what a little 100 foot wide space rock can do. But Americans with a personal cache of gold would still have had value, because there is always a large number of people everywhere willing to pay a high price for it, whether that price would be in surviving currencies, or in food, shelter, and the necesseties of life.
Actually, Wired magazine pointed out recently that blowing up Washington would probably cause a massive INCREASE in the effectiveness of our military--and because Constitutional succession would come into play very quickly, we would have something resembling a government again, but without the same sort of metaphorical inbreeding. Wiping out DC would thus tend to make the government AND military much more efficient (and hence effective), actually INCREASE the value of our money.