People use oranges and apples instead of water to help keep them hydrated. Stop and give them water breaks like you would with dogs or cats. And do the clean out thing with the poo trays under the cages.
When we moved cross country - 3 days- with dogs and cats, I used those dosposable litter pans (should be good for the chickens too. and for the dogs, I lined an area in the car with the puppy training pads. (never did need those though). I traveled daytime. But with chickens, I would drive at night mostly, I think. Would be a lot less hassle than feeding and watering them constantly.
But if you stop over at night or day, what can you do with them. Where could you stop. You may need to figure something out or drive through. So how many hour drive is it going to be.
There's a person on here that drove a car full of ducks (big ones) from texas to Colorado, I think. So ya, it can be done.
edited: ok so around 20+ hours. I think the duck traveler drove till got tired, used truck stops or whatever, rested for a few hours and drove on. Said it really wasn't as bad as expected. Was a teacher, delivering mostly grown Muscovies to Dad's after the class had hatched them until they could be brought. I have done similar drive straight throughs when younger, with kids, dogs and cats across most of the country. You'll be tired when you get there is all. Plan on that.
Most Best Western's take dogs and cats, check with them and let us know. If they are caged with trays, don't see why not. Pick one North of Sacramento for a half way point and call and see what they say. Serious. Or leave the chickens in the car and go get some sleep. Tell them people on BYC want to know. Cause we do. What do Chicken Show people do? Maybe they could travel to farther shows if Best Western would take Chickens. Just an idea and for all I know they just might, they deal with people that travel with animals.