Library of Congress is a nice quick tour that would be nice for a short layover. Lines are not as bad as other more popular places and it is a short walk from Union Station.
Also, there's a theater on the lower level by the food court if you'd like to see a movie.
Sadly, it closed a few weeks ago.
Good riddance if you ask me, that place was a dump
One thing I always love doing in DC is touring the Capitol building... if you call ahead to your Senator or Representative's office, you can request a "Staff Led Tour" which allows you to skip the LOOOONG lines at the visitor center. Plus, with the smaller groups in the Staff Led tours, you stand a better chance of getting all of your questions answered... and sometimes your tour can include things not typically included in the public tour. For example, I was able to go onto the House Floor during one of the Staff Led tours my Representative's office set up (The House wasn't in session, but it was still amazing!) I also got to ride on one branch of the Capitol Subway during one of my tours
My fiancee works in the CVC, this is a great idea - you can also ask for a "Dome Tour". They're lead by the actual member (not a staffer) and you get to go up into the dome, and outside up near the top. I've never done one, but she's scheduled to go on one for training in the near future and rubs it in my face constantly.
It's highly unlikely that the Member will actually have time to do it, but it can never hurt to ask.
The dome tour is the best tour you can do in DC. Its something that not many people get to see. I was a Page for Strom Thurmond so taking the trolley back and forth from the Russell building to the Capital became no biggie, but the dome tour sticks out as the most interesting thing I saw while working up there. Its amazing to see the fresco up close and then the outside view of DC is hard to beat. On my tour we didn't have a congressman or senator leading it though, it was just some guy that worked at the Capital. You are right that it is a longshot.