We're renting a minivan for one day in November from National. Pick up location is at the Dolphin Hotel. The estimated price, including all the surcharges and taxes, but not insurance, is $53. 52. We're DC members and the price includes a 20% DC discount. I'm sure the one day price would be lower for a smaller class car and of course, prices do vary by season. Anyway, thought that might give you some idea.
You could easily check rates for your day and car type on National's web site - no obligation to make a reservation unless you find a deal you can live with. I think your idea of a one day rental will turn out to be less expensive and more convenient than taking a cab. Our auto insurance covers rentals, so we do not take the insurance offered by the rental companies. You will need to check with your agent to be sure your policy covers rentals. Not all policies do.
Good Luck and Enjoy your trip!