This might help. It is not directly inside DC, but close proximity. Nice rooms. Have cooking facilities, etc. Really cheap. It is inside a base housing compound.
You might also want to try lodging options on Andrews. We stayed there many years ago on short notice. I think it was more for those transfering in and out, but they did have an opening and allowed us to stay there that night.
My son is stationed in the D.C. area and lives at Ft. Belvoir, VA. about 15 miles south of D.C. Ft. Belvoir has nice lodging for military and their family. The phone numbers are:
Front Desk 703-704-8300
Reservations 800-295-9750 or 703-704-8600
Breakfast is provided each morning. Ft. Belvoir is 7 miles south of the Huntington Metro Rail Station which is an easy way to visit the city without the hassel of parking.