Many years ago we took US 30 from the Colorado border to Iowa boarder. (Much of the route followed the old Pony Express route and the Oregon Trail.)
The whole way had a wide shoulder.
The western half had low traffic. The eastern half was busier but very doable, except in a couple of cities.
There was a town every 15 miles with basic services.
Check the prevailing wind for the time you plan to ride. Winds in Nebraska can really be a moral breaker.