In June 2011, we left DC at 4PM, bound for Glacier National Park. The first night we made it to just past Indianapolis by about 3AM, a little over 600 miles. The next morning, we started around 10AM and made it to just outside Mitchell SD around midnight, a little over 800 miles. The next day we made it to the badlands by noon where we over-nighted, then to Custer State Park where we spent three nights. We had the advantage of no children in the car. We also don't mind driving if we need to, to get where we are going. We also spent 3 nights in Yellowstone, 4 nights in Glacier, 2 nights in Teddy Roosevelt, a night near the Dells in Wisconsin, and two other nights at various spots on the road in Montana. We arrived back in DC on what would have been our 19th night.
It can be done, it really just depends on your tolerance levels. DH and I have very high tolerances and have been traveling like this for years. If we know that we will have a few days down time we can easily crunch out 700 miles. We did it again in September 2012, going 700 miles on day one and 850 miles on day 2. Day 3 we were in Mesa Verde.
Just a heads up though - we can drive these times because we stop at rest stops, not campgrounds. Hooking, unhooking, packing, unpacking - entirely too much time and trouble. But, we don't have kids, don't have to open our slides, and can carry enough water for a shower and coffee. Staying at a campground, you need to arrive by 7PM (courtesy) and be ready to leave again by 6AM just to get enough hours to cover 600-700 miles.