ودي بشقق مفروشه .. واشنطن دي سي

living in the DC area is very expensive even for a short time.
Hotels are not you best choice. but check on orbitz.com for deals.
Also you may want to check this furnished apartment complex (Virginian Suites). it is in Rossyln, Virginia. across the river from DC. it is walking distance and you can use the Metro (the train) the building is NOT fancy , just your average furnished places. they have short stay and extended stay too.

http://www.virginiansuites.com/extended_stay/