I will be embarking on just such a trip in about 4 weeks: just over 2,000 miles each way. Leesburg, VA to Chinle, AZ and back.
I've driven across the US many times. Most miles covered in one day: 1,000. Little Rock Arkansas to Las Cruces, New Mexico across the width of Texas. Took 18 hours, but I really don't care for West Texas and was determined to get beyond it before stopping.
Every other time across, I taken major highways. This time, I'm not in a great hurry, so I'm considering avoiding highways and taking rural routes to better see the country.