Oregon mouse is right, as usual. Pedestrians are barred from Interstates everywhere. But if you are lucky, you will get a ride in a nice air conditioned police car that will carry you forward. Some sections of interstates and multi land highways are open to bicycles; but it is extremely unpleasant and dangerous. Walking an interstate would be my version of hell on wheels.

Interstates are diabolically,and cleverly, designed to expose you to absolutely the flattest, most boring parts of whatever country they traverse.

Just for reference on water. I once had to start a hike in Tucson at 1PM, temperature 91 degrees. I ran through two gallons of water in five hours, at which point I was still clinically dehydrated. And I was a local resident, fully acclimated. We were hiking very fast, though.

I would recommend crossing the country from one good long trail to another, and using a bus ticket or whatever to skip the boring bits in between. My 2 cents.