You shouldn't have any problem with water stops/availability up to Fallon. After you leave Fallon the next place for available water and food will be Middlegate which is about 55 miles. There is a neat old store with a bar and grill and a limited selection of groceries. They also have small number of rooms. I haven't stayed in them so I can't say what they look like. If you opt for the alternate route after Middlegate there aren't any water stops until you get to Austin - 60 miles.
The next place for water is Cold Springs which is about 11 miles from Middlegate. There used to be a gas station and limited store there but it burned down several years ago. I hear they have been building a new store that is supposed to be finished by now but I haven't been by there since September so I don't know if it's done. They also have some rooms for rent.
Then next place for food/water/rooms is Austin. It is about 45 miles from Cold Springs. There are a couple of bar and grills as well as three motels (Pony Canyon, Lincoln, and Mountain). There is also a B&B in town that is wonderful. Can't remember the name but anyone in town will tell you where its at and who to call. The two gas stations have a limited food selection.
After Austin the next water stop other than the campground at Bob Scott Summit is the town of Eureka about 70 miles away. There are two motels and a good grocery store. I recommend the Best Western. It has a hot tub and a pool as well as a so so breakfast.
The next place for water/food/motel is Ely about 75 miles away. It has several motels, restaurants, and grocery stores.
After you leave Ely the next water stop is at Majors Junction about 30 miles away. I haven't stopped there so I don't know what they have to offer. Baker is about 35 miles away and it has a small grocery store (owner is NOT very friendly) and a small motel (Silver Jack) with a great little wine bar and the owners are wonderful.
You can also stay at the Border Inn on Hwy 6/50. It has a restaurant/motel and a limited grocery store and the owners are real nice. The rooms are ok. The next stop on Hwy 50/6 is Delta. As I recall it is 80 miles of nothing.
If you can carry 3 water bottles and have a 100 oz Camelback you should be able to make it. However if it is really hot you may find you need to carry more water. If you leave early in the morning you should be able to get to your next motel before it gets too hot.