Even though a federal government shutdown is all but certain, it doesn't mean there aren't interesting and exciting things for visitors to see and do.
Yes, it's true that the Smithsonian museums and other major attractions like the Washington Monument will be closed if the government closes. And yes the Cherry Blossom Festival will be cancelled if the government closes. But there are still museums like the Newseum and the National Museum of Crime and Punishment that are privately funded and will remain open during a shutdown. The only drawback is that most of these privately-funded attractions are partly funded by their visitors. So expect to pay some entrance fees.
Check out my list of other fun stuff to do this weekend that won't be affected by the government shutdown.