There is confusing information. DCA website says they used to have it flyreagan.com - Baggage Storage through a vendor called Baghop but that it is discontinued. Baghop website does not seem to work but they have a phone number (703) 944-2229 and other travel webpages indicate they are open.

Another possibility, if you have access to an airline lounge, is to drop the luggage there.

You might call airport information desk and ask to be certain. Phone: (703) 417-1806