The Congressmen were held in high regards by the residents of Washington, and routinely beat teams from Virginia and Maryland. John Henry Eden talks about rebuilding the team sometime in the future,  though his monologue is likely propaganda for the Enclave's personal vision of the "good old" United States. 
The Capital Congressmen are mentioned in Fallout 3.
Behind the scenes Edit
In the real world, Washington, D.C.'s baseball team is the Washington Nationals, but most likely the Washington Congressmen is a reference to the baseball team that represented Washington D.C. in the 1940s and 50s, the Washington Senators.