You can drive from Houston to DC without stopping (except for gas) Leave at 4am and you'll be there 2am the next day just in time to sleep. San Diego , CA to Dallas, TX took 21 hours, a box of Golden Ghrams and about a 6 pack of coke.
I stopped every 350 miles. 1357 miles. you have 1406 miles, so expect 22 hours. If you traded off with one person driving and slept in the driver's seat you'd have no problem. I didn't have a passenger so I had to drive the whole way. I left at 2pm and got there at 11am the next day. It was the winter that the hailbop commet was easily seen, I didn't take it as a bad omen.
BTW, driving at night is dangerous, so maybe split it between two days, one hotel.
Heck I went from D.C. to San Diego in 3 days. And I was taking my time.