I'll second the car rental recommendation. Just wait out rush hour until 9a or so, and then it's a straight shot into the city. Just follow 66 all the way in to Constitution (Rt 50). About 2 minutes down Constitution and you'll be in front of the White House (and the Lincoln Memorial will be to your immediate right when you get off the highway).

I'd also recommend getting back on the highway at 2p - you never know when 66 or the Beltway will back up for no particular reason.