What to do in Washington DC for a day?

Since you only have one day I would say to dish out the extra money and take the Big Bus Tour. A lot of the sites are downtown but ones like the Lincoln Memorial, Jefferson Memorial and Arlington Cemetary are not decent walking distance *take some time). To me the Big Bus would be faster. I didn't take it last year so I missed a couple of sites.

About the White house:
Check the web site on how to apply for a tour. Keep in mind your limited time.
Otherwise, you can stop at the fence to take some photos. Consider stopping by the visitor center.

White House Tour
Lincoln Memorial
Smithsonian Museum
Martin Luther King Jr. Memorial
Holocaust Memorial Museum

In addition to the good answers you already have, the National Archives are interesting with a lot of good exhibits: http://www.archives.gov/dc-metro/washington/ The Washington National Cathedral or Basilica of the National Shrine of the Immaculate Conceptioncan also be interesting. You might find other ideas here: http://washington.org/

Smithsonian
US Mint
White House
the major memorials (Lincoln etc.)

DC is IMHO a bit of a dump (horrible climate, full of politicians, etc.) but for a day or two it can be kind of fun, if you're into sightseeing.

Bob gave you some good ideas. I'd also suggest asking them what they want to do--they're sure to have some ideas. Maybe they want to see a baseball game, or go shopping, or eat at Hard Rock Cafe or see the Spy Museum.

Take them to the National Mall. There they can see the Washington, Monument and from there see the White House, they can also see the Capitol Building and the Lincoln Memorial.
You can take them to the Smithsonian Castle, and maybe one or two of the Smithsonian Museums. You can remind them that the Mr. Smithson was a British citizen and never came to America and donated the money for the museums.

Read the below source and get ideas.