In my opinion grinding out day after day on the interstate isn't much fun. The Interstate on a bike is fun for about two hours then it gets really boring.
Grab a map and look for towns etc, you might just be surprised, its one of the parts of N.A I have not been around but parts of Utah are fairly barren as well and I had to go out of my way to make it hard to have enough gas.
The only places\times I'd be worried about (and ever are worried anymore) is in a tourist only area, at night or on a national holiday that lands on a sunday.
I'm not worried and I tour on an R1. If you happen to come near an area where you think you'll be worried going into, such as crossing a barren place in the middle of the night on a sunday national holiday. Stop and buy some 2 liter bottles, empty the water out of them and replace it with gas they sell gas in those bottles in some countries so its going to be fine for the 20-60 minutes it has to sit in your bag for. Otherwise, slow down the odd time to make sure you will have ample gas.
In America the land of plentiful gas and 24 hour stop and go's.
Besides if you do run out it makes for a better story.
The lesson, take your time, don't rush the trip. Two weeks? Cross country? You will not be able to accomplish this trip in your allotted time unless you want to hate life for the entirety of the ride, and don't actually want to experience any of the places you go. That's not even taking into account bike maintenance, weather, days of being hungover and wanting to stay in a place because it's awesome.
Six hundred or more miles a day regardless of weather will be pretty tiring if you plan on stopping to see the sights and relax at night. Doable, just understand its not the same as driving 600 miles in a car.
In '03 I did a long trip on a R6, needless to say tt took me two weeks to get the knots out of my back, the wrist pain to go go away, and the knee stiffness to subside.
Not worth it.
Not in the least.
Then I bought a V-Strom for a trip from Florida to Dallas and back and it was actually enjoyable. I'm not some fatass that can't use my legs to mitigate fatigue on a sportbike, it's just the nature of the beast.
I would definitely suggest looking at at least some risers and adjusting the peg height if you want to go with a sportbike.