Just did 16 weeks traveling the west. In Nebraska, don't remember any issues. South Dakota south of Badlands did have road closures. Signs for road closures were vague about where they started so we back tracked and took a slightly longer less scenic route down the interstate going to Badlands NP. We learned to look at each state's DOT website for road closures. While we didn't have any other Indian Reservation issues, we did have to change our route around one road closure and find a more local backroad route around a bridge closing.
One thing to remember, a state highway detour will only use state highways so there could be a much shorter detour they aren't allowed to use. A county road detour can use any road for the detours. In our case of the bridge closing, I wouldn't recommend the two track dirt road we took but a few of the locals were using it making it a very interesting 2-way traffic road through the gullies and mountains of south eastern Colorado but 10 miles of that saved about 120 miles of pavement.