1,000+ miles in a day is a hard ride. I believe a man can do just about anything he sets his mind to, but it's a hard, hard day and you're gonna be sitting in traffic more than a few times on that trip.
You will be destroyed at the end of it. I'd recommend finding someplace midway to sleep for 4-5 hours and then taking off again. If you haul it straight through, you're gonna lose a day anyway when you finally do get out of the saddle and give in to the exhaustion.
That's what I'd do, anyway. I do 730 miles one way each summer to hang out with friends, and I'd hate to be staring another 400 miles in the face at what is normally the end of that trip (right around 13 hours usually).
Good luck either way! Be safe and have fun.