You'll have no problems finding parking in December on a Saturday. In fact, it may be quite empty.

Only concerns could be that 1) it could be pretty cool (not likely to be snow, but it does happen in december), and 2) its going to be getting dark by 5:00 pm. By the time you get in your car (assuming an on-time arrival) its going to be 5:30 pm which means close to pitch black...

And since we're talking a Saturday night, I would strongly advise against Metro because with the system being as f**ked as it is now, its only going to be worse on a Saturday. Indeed, from 12/6 to 12/24, Metro is going to be SHUT down on the Blue line from Pentagon to Rosslyn - meaning your access to any Mall monuments is going to be quite circuitous.