At times we carried two gallons of water each. Most cyclist we saw ran out of water on the section between Milford, UT and Baker NV. We left Milford at 3am at made it to the Border Inn on Hwy 50 (off route) at about 1pm. Two gallons each was sufficient for us given the early start. We had called ahead to Baker and the accommodations were all booked so we went to the Border Inn. Never having seen the accommodations in Baker I have to believe they are a better choice than the Border Inn, but the Border Inn did have food and lodging.
I would highly recommend you strive to be self sufficient. There are few if any opportunities for water between towns for many sections. Other cyclist told us they spent many hours besides the side of the road trying to get someone to stop when they ran out of water. People seem to be afraid to stop on some of the lonely sections such as the one between Baker and Milford, and there is very little traffic, I seem to remember one car an hour. Our strategy of starting early (rolling between 3-5am) and arriving around noon worked well. The sun rises are spectacular. Carry lots of water anyway, although you will use less when you ride in the cooler parts of the day/night. Of course another strategy would be not to ride in July (or August)!
Be aware of the possibility rattlesnakes on the shoulder or road. They can be difficult to spot off the road in the dirt and brush, at times you may want to just pee in the road.