Careful, though: the paid storage room is ferociously expensive. I have never seen a costlier one. Maybe $5 an HOUR?!!!!
We don't know where you are coming from or going to, but could you use the checked baggage service as storage? Or get into the Metropolitan Lounge?
Example: you are going from Philadelphia to, wherever. Check your bag in PHL to DC (even if your ticket is to a point beyond, you can still do this). It will go to DC on a long-distance train, and you pick it up there at the end of your day in DC for your ongoing travel. We can give you better advice if we know your real travel schedule and itinerary.
If you are in a sleeper (or Acela 1st class), use the Metropolitan lounge, which has a free storage room.
Hauling a bag around town is never fun, and in DC it does, indeed, keep you out of a bunch of buildings.