You might be surprised at how much a well can supply. There aren't many rivers to speak of across Nebraska, Kansas and Oklahoma, but most of those states are well-irrigated from the massive aquifer underneath the Great Plains. A little too well-irrigated, really. That aquifer isn't recharging as quickly as the water is removed.

Also, just because a river isn't shown on the map doesn't mean it isn't there. A map of an area this size is only likely to show the most major watercourses, specifically those that are navigable or are wide/deep enough to serve as barriers.

Inhabitants of very arid areas can get moisture in nontraditional ways, too. There is a nomadic pastoralist culture in North Africa somewhere that gets moisture for drinking from bleeding their cattle. And they wash their hands in the cows' urine. Of course, they don't form settlements, so that's of limited usefulness for this particular question, but the point is not to underestimate peoples' ability to get what they need from environments that seem inhospitable.