You're right - both of those museums will be closed. Darn it!
The National Gallery of Art, however, will be open. I checked to make sure there's no construction problems. Here's a link:
http://www.nga.gov/ginfo/renovation.shtm
Other Washington museums:
http://www.asia.si.edu/exhibitions/default.htm (includes a Whistler exhibition)
http://americanart.si.edu/collections/exhibitions.cfml (Treasures from the Smithsonian American Art Museum)
http://www.corcoran.org/ (modern art)
http://www.phillipscollection.org/ (modern art)