You won't put enough miles on the car for the price of gas to matter at all.

But agree with others the hassle of parking and navigating isn't worth it. I'd use a combination of metro, taxis, and uber to make it happen. Traffic won't be horrible, as noted, although Saturday night in December means holiday parties and traffic can be bad at that point (and Uber a tad expensive).

For example, you could take Metro to hotel in city, catch a taxi to Washington Monument (Constitution Ave side), take a walk there, and keep going past tidal basis to Jefferson. Then catch a taxi or Uber to Lincoln memorial, and proceed on foot from there to a metro station or another uber. Lots of permutations involving a combo of ideas.