DC's Winter Restaurant Week is January 11 to 17, but there isn't much local participation. The deal is, you get a three course meal for $20.10 at lunch or $35.10 at dinner, not including drinks. Could be a good deal and a good way to check out some local spots.
However, in our neighborhood only Eatonville at 14th and Florida is participating, although Policy on 14th Street and T is in, as is The Grill from Ipanema in Adams Morgan.
I'm kind of surprised places like CommonWealth, The Heights, and Social aren't in it, but maybe that's because they're really not that expensive anyway -- you might have trouble finding three courses that are much more than $35 anyway -- just take a look at all their menus. Most Restaurant Week places are generally fancier joints that folks don't normally go to (and thus, why some restaurants don't like participating).