Excellent question. I hope someone with more knowledge vis a vis the US student loan system chimes in, but I'll add where I can.
To begin with, in the US, it's important to distinguish federal loans from those issued by the private sector. The former are issued by the government, the latter by private institutions (banks, et al).
Federal loans : The IBR (income based repayment) plan was recently introduced [1]. It appears similar to the UK plan, except the implementation details are different (15% of income over 25 years). There are of course eligibility requirements that (shock of shocks) are not always crystal clear [4]
Private loans : nothing whatsoever AFAIK, nor much planned future legislation
Lastly, it's important to note that both public and private US student loans are notoriously difficult to have discharged, including in the event of bankruptcy. The bar is set high enough to almost be considered de-facto impossible [5] (opinion).
This, IMO, makes the astronomically high figure presented here all the more alarming. An affordable education is possible in this country, but we haven't been good at educating the public in this regard (ironically, I guess).
For a general breakdown on the differences between federal & private loans, see the linked chart [6]. While I guess I should have known this already, I was surprised to note that some privately issued loans come bundled with pre-payment penalties.
[1] http://studentaid.ed.gov/repay-loans/understand/plans/income...
[2] http://en.wikipedia.org/wiki/Income-Based_Repayment
[3] http://articles.chicagotribune.com/2013-02-12/business/sns-2...
[4] http://www.nytimes.com/2011/10/27/your-money/student-loans/e...
[5] http://www.nytimes.com/2012/09/01/business/shedding-student-...
[6] http://studentaid.ed.gov/types/loans/federal-vs-private