The overlay with Republican-majority voting is....interesting.

"When Chetty and his colleagues first published this chart, earlier this summer, it got a lot of attention, and that’s not surprising. The map show the areas of low social mobility to be concentrated largely in the South and the industrial Midwest. Generally speaking, these are areas that have high numbers of African-American residents and a lot of residential segregation, which has inevitably focused attention on the roles race and segregation play in sustaining a caste-like system, in which those who start out at the bottom tend to stay there. Chetty noted that these two factors certainly appear to play a role, but he also pointed out another couple of interesting facts. 

"In these low mobility areas, it isn’t just black residents who tend to get stuck. Whites, too, exhibit low levels of social mobility. In states like Georgia, Mississippi, and South Carolina, poor white children tend to grow up into poor white adults. Secondly, regardless of race, the level of income inequality itself seems to play an important role in determining levels of social mobility. In places where income is divided very unequally, and poorer groups get only a small slice of the pie, very few people manage to start at the bottom and end up at the top. 

 There's five more charts- and an interesting article- in The current New Yorker. Together, they show how the US has become increasingly divided into the Haves and Have-Nots.