Check airbnb. If you haven't been to DC before, make sure you look for something that's close to a stop on the Metro system (see wmata.com for maps and other info). If you won't have a car, you can get around but you sometimes have to plan well, especially with where you'll be staying. Out in the suburbs, for instance, there are bus systems but many of them only run during commuting hours at infrequent intervals. Finding a place near downtown would make things easy but you can probably save some money by finding a place further out, but still a short walk to the Metro.
If you plan on riding Metro a lot while you're here, you might save a little bit of money buy getting SmartTrip cards. They have an upfront cost, but paper farecards are $1 more expensive per trip, I believe.
Our house is pretty full and we're looking to get out of the east coast, so we might not even be here in late March.