There actually seems to be quite a lot of evidence for the US having a low social mobility. I recall some articles a while back in The Economist about it [1][2], something that surprised me a few years ago. Not any more. It doesn't take long to find many reports detailing this.

[1] http://www.economist.com/news/leaders/21571417-how-prevent-v...

[2] http://www.economist.com/node/21571399