I think you -could- but I don’t know how satisfying it would be. Check out the free highlights tours offered by the museums. I live here and that’s a great way to get a taste of the museum’s offerings in like an hour without getting overwhelmed.

DC has lots of great museums, but also fun neighborhoods and other things to see. (Ballpark, hockey, waterfront, Capitol building, embassies, bars, restaurants!) You might miss something awesome by just limiting yourself to museums for a week.