Tuesday thru Friday AFTER Memorial Day likely won't be much worse than any other week. I live right outside DC and my job takes me into DC on occasion. Driving in DC always stinks. Holidays are a little worse, but rarely is traffic ever considered "better".
I think Memorial Day week is a pretty decent time to go. Its late enough in the spring that hopefully it won't be raining, but not quite summer so it won't be humid and miserably hot.
I would encourage you to take Metro if possible, just to save time trying to find parking. Parking can be a crapshoot, especially near the memorials. It is a great experience to visit though, so I hope you get to come enjoy the sights!