Anyway, the fastest route is I-90 to Chicago and onto I-76 and on into Washington.
I hate to disagree with Mark, but that route will catch you up in Chicago traffic and cost you a ton in tolls. This route is only about an hour longer and has zero tolls:

I-29 to I-880 to I-80 to Davenport IA
I-74 to Indy, take the I-465 south bypass
I-70 to Columbus, take the I-270 south bypass
I-70 to Wheeling, take the I-470 bypass
I-70 to Washington PA
I-79 to Morgantown WV
I-68 to Hancock MD
I-70 to Frederick
I-270 into the DC area

If at all possible, take at least part of a 3rd day.