I've run back and forth from the Boston area to Missoula, Montana time and again. Its 2740 miles door to door, and I've done about 28,000 miles on that run. The longest I ever drove in a shot was 1700 miles -- from Missoula, MT, to Ft. Wayne IN. I don't recommend that. I emerged from that run with some wisdom that I may not have had prior.
Normally, I'd throw the stuff in the car -- many of these trips were done with a Deep Jewel Green 1994 5-speed Taurus SHO with a mocha interior, the perfect tool for the job -- fill the tank, grab a Lipton iced tea with lemon (only the kind in the glass bottle), ensure I had plenty of cigarettes, and hit the road. A note about packing -- the more I did this run, the more I realized the virtues of packing light -- no obstructed sightlines allowed; everything goes in the trunk.
I've left out the obvious, but mention them as a formality. Change your oil and filter before you leave. Driving cross country is an unbeatable opportunity to clean an engine. Having clean oil allows you to avail yourself of this. Your car will be faster when the trip is done, provided it is properly tuned. Make sure your coolant is fresh, too.
Don't push too hard. I normally divided my trip into three legs -- Boston to Ft. Wayne (970 miles), Ft. Wayne to Rapid City, SD (1100 miles) and Rapid City to Missoula (670 miles). Reverse for the trip east. I may have been a bit gung ho, too -- so keep that in mind. One time, I came back without a working starter. That required a few KOER refuelings and some creative parking at night so that I could do a rolling jump start the next day.
Most of all, enjoy it. If you're getting burnt out, stop and have a bite and a drink. I recommend eschewing coffee from your long distance lexicon. Also, no beers. Even one or two would have you feeling wiped out not far down the road. I never took the chance, for when your running thousands of miles, you are really on the road.