PMI Parking has a garage @ 18th/Desales NW is the cheapest I know of in town. $12 overnight rate, $20 for 24 hrs.
They have many other locations that might be more convenient to your hotel, too, but the Desales street location is the cheapest I think.
PMI Parking Garage Map
But parking in DC is expensive, period. If you don't want to pay, leave the car at home. You won't really need it while you're here anyway.