What is DC like at Christmas?
 

We are thinking of going to Washington over Christmas . . . we will probably arrive on Christmas Day. Will it be really boring over the holidays, with everything closed and Congress in recess?

A million or more people live in/around DC. They go to work, restaurants, movies, theater, museums, concerts, etc. even when Congress is not in session.
Most attractions are closed on Dec 25, but the lovely Botanical Garden at the bottom of Capitol Hill is open that day.
Restaurants open on the 25th will be those in hotels and some ethnic places, notably Chinese. Use Open Table to make dinner reservations.
The advantage to visiting at this time is the lack of convention business means good rates on hotel rooms.
Consult washingtonpost.com, washingtoncitypaper.com and similar for listing of events.

Another nice activity for Christmas Day is to go see the National Christmas Tree and all the state Christmas trees on the Ellipse. It will probably be crowded, especially if the weather is nice, but it's still worth doing that day. And, of course, you can go to all the open air monuments.
After Christmas Day, everything will be open again and it's not at all boring here over the holidays.

Thank you for your replies. I am so encouraged! We are already planning our trip.

Because Christmas Day is the one day that all the museums are closed, you might want to think about a movie. Both Georgetown and Gallery Place have multiplexes and many will be crowded after dinner time. Dress for winter. Tidal Basin and monuments are lovely but can be icy cold. After December 25 the city will be booming and the Smithsonian and other touristl sites will be busy. You might want to check with ticketmaster for timed tickets to the Washington Monument. You only pay a small service fee for the reservation. Also check with your representative if you want scheduled visits to the Capitol, Library of Congress, Supreme Court, Bureau of Engraving and Printing. I think you've left it for a little late, but there might be some openings.

Mount Vernon is open on Christmas Day.

There's a free Christmas jazz concert on the Millenium stage at the Kennedy Center in the evening and a choir concert at the National Harbor - I don't know if the water taxi runs on Christmas, but you could incorporate that into a visit to Mount Vernon, if it does.