Offshore developers: how do you break into U.S. market?

The question is in the headline. When you are offshore, you are tied to job sites like www.odesk.com where you have to compete with people from low cost countries like India, which drives rates down, forming a low-cost market of its own (and with these providers frequently scamming their clients, these low costs seem to be justified due to increased risks customers have to carry). Essentially there are no jobs at over $35 an hour or so.

Everyone knows that these are below bottom rate on U.S. market, and for someone knowing his job, there must be a way to break in there - i mean both individuals and companies. Who tried? Can you share some of your experience?