I've done these... many times.
Here's how I do it, pick and choose what you're comfortable with.
On the interstate, I'll do 16 hours, leaving 7.5 to sleep. This is approximately a thousand miles. When my destination is at the end of the day, I'll push to 1200-1300. This reduces stops. (Okay, being honest, these days I do 1100-1200 by default. I've improved.)
Get a big pack of water bottles, usually 24 or 36 for under five bucks. Yes, bottled water is wasteful, except in this one instance. Either prepare some food to eat, or stop at grocery stores along the way. There are chains (lucky, safeway, etc) that sell this really big sandwich for $8 that lasts about a full day... or two.
http://i.imgur.com/ER3QWea.jpegEasy mode: stop in motels. I like motel 6 or super 8 for how cheap they are. There are cheaper. Note that their prices in the middle of the country are seemingly random: tiny town $40, tiny town 60 miles later $70. Why? Because. Ask if they have night rates (probably not.) Use AAA discounts if they offer them. If you show up at midnight, they know the room will otherwise go un-occupied, and are more willing to bargain. Politeness obviously is mandatory.
Hard mode: take a sleeping bag, stop in rest areas / scenic overlooks / random pull-outs. I did this for a whole week over thanksgiving, and for some days in Alaska / Canada / along the pacific. Nobody has ever bothered me even when stopping in places that have signs not permitting it. If anyone bothers you... "yes sir, sorry sir, I did not realize, I am leaving now, I will be out of your way momentarily." Get a 0 degree F sleeping bag for $50 on amazon, there is one that is excellent. The first shower/bath when you get back to civilization will be glorious.
This results in my expenses being gas + $5 a day, or less.
I've done, at this point... almost 30 separate days of 1000+ miles or 16+ hours on the road. I've lost track now. This part of the advice, while it does save you money, is not for everyone. My first cross-country drive, Boston to San Francisco bay area, I budgeted 8-10-9-7-7-7 hour days, because I figured the first day wasn't a full day, then a full day, then I would get tired. I ended up doing 8-10-14-16. Turns out that once you're out of populated areas, driving becomes really easy if you're good at sitting still and paying attention. My record is 18+21 hours back to back. Try it but don't push it to save a few dollars. You may end up making Texas to Virginia in two days. I made El Paso to just north of DC in two days. But if you start feeling like you're losing it, just pay the $60 for a motel and get a good night's sleep.
The thing nobody tells you about driving that direction is that you lose two hours of time. Factor that into your math.