Some hotels near IAD can be very cheap - dependent on the time of week and the time of year. I've snagged the Westin Dulles for less than $90 for night getaways with the family.

Only concern is getting to the hotel from DCA. The savings might be lost in cabbing there.

If I could find a cheap hotel near DCA, I'd almost rather the OP do that and then be able to take Metro from Crystal City/Pentagon City to IAD (transferring to Washington Flyer at Wiehle Ave.).