Uncertain from your post whether you're doing this drive entirely on your own, but having done a lot of solo intra-state driving down here in Australia (where the states are BIG relative to the US), and also attempting to lap New Zealand in a week with my 2 brothers, I have some driving survival tips:
Allow generous amounts of time to get anywhere - particularly where your routes encompass single carriage-way highways through any kind of hilly or mountainous terrain (ie: New Zealand "highways"), the distances may seem short in miles, but if you're unable to maintain a constant high speed, the time it takes to cover those miles zooms up far more than you realise.
For fuck's sake, make sure you stop and rest and *stretch*, particularly if doing all or most of the driving on your own. This goes double if you use a vehicle with less than stellar seating design. If at all possible, allow at least a day's respite between long-haul distances. I once had to do a non-stop dash of some 500kms and come back the next morning in my 94 Pulsar, and I could barely move by the end of it.
Ensure you have sufficient WATER (or fruit juice/whatever) within easy reach at all times. If you have the heater or air-con on, blowing in your face for hours at a stretch, you will dehydrate like so much desert sand in a very short time. Proper hydration helps you get enough oxygen to your brain, meaning you won't get as fatigued as quickly.
Similarly, stopping for "real" food, vs surviving on "travel snacks" is also a lot better for your sanity and general wellbeing.
As has been mentioned above, if you are in the slightest doubt, GET PETROL/GAS/FOSSIL FUEL before you keep driving.
If you're on your own, helps to have your driving music sorted in a format that can be adjusted with one hand and peripheral vision only.
If you're hiring a car, I'd try and ensure that your cell-phone has an in-car charger that is adaptable/usable with the make of that car. I've only ever used my own/brother's car for these sorts of things and we've got car-kits already installed so I'm not entirely au fait with the current in-car chargers as accesories situation. Disregard if irrelevant.
Last of all, if you're taking your own car, check your tyres (tread and air pressure), oil, water, and wiper blades before you go, and if you stop for a while somewhere (like, days or weeks), again before you depart. Take some battery jumper-leads and a torch and a first aid kit too.
Sorry if any of this comes over as condescending/patronising, but so many otherwise sensible people (inc myself) can tend to overlook really simple basic things that can help prevent being stranded on the middle of some godforsaken stretch of bitumen.