We drove from DC to the Badlands in two days. First overnight was in Indiana, second was in South Dakota. On the first day, we left our house at 4PM and stopped at 3AM (we prefer to drive at night). Second day we drove from about 10AM to midnight. We slept in a truck stop the first night (horrible) and a rest area the second night (wonderful). We left on a friday afternoon and were in Badlands National Park by noon on Sunday. We were a little cranky by the time we pulled into Badlands but a good meal and a short nap and we were ready to roll. We spent the late afternoon hiking the area.
If you don't count the Friday, our entire trip was 16 days - three weekends plus two midweeks. We ended up going from there to Custer State Park, Yellowstone, Glacier, and Teddy Roosevelt.
Would I do it again? Yes, we did it this past September when we drove from DC to Colorado and then on to Utah and Arizona. But, we took three weeks as we had more to see.
A couple of notes: the longer you are on the road, the more you want to stop. Try to bust out the miles earlier in the day. When you do stop, get out and walk around. An extra ten minutes out of the truck will allow you to drive further on the next leg. Have pre-planned stop locations. It's easier to drive another 30 miles when you know you will be stopping rather than having to hunt for the next stop. When all else fails, listen to talk radio - Howard Stern has gotten us through many a miles.
Good Luck and enjoy your trip!