What months, and do you wish to reach either the Gulf or West coasts? Assuming you'll be on the road for the entire 2 to 3 weeks, what daily mileage rate are you comfortable doing? 800 miles isn't difficult with 2 guys driving on Interstates, but then there's little time to stop and sightsee, and taking local roads is less of an option.
400 miles on average allows for more diversions, and 14 to 21 days equals 5,600 to 8,400 miles, enough to reach the West Coast from DC and back. Subtract from those distances a day's travel whenever you might stay a full day or more at a location, say at Yellowstone. BTW, much of the western US parks system areas are closed in winter months, going into reduced operation.
The passes over the northern Rockies also become problematic, often impassable for days.