Also check out 18F [1], which focuses on pushing forward how tech and the government work together. They run a 12-month Presidential Innovation Fellows program [2] which works more intensely on innovating with specific groups within the federal government. USDS is more focused on modernizing and ensuring some basic technical functionality of a lot of the core aspects of the government (which is incredibly important and impactful, but is less about innovation -- see a comparison here [3]).
Make sure you have got a plan for 4 months as you work your way through this hiring pipeline. In other words, if you want to change jobs in December, and start working at 18F, you should be applying right now.
It is an extremely lengthy process, unfortunately.
[1] https://18f.gsa.gov/
[2] https://www.whitehouse.gov/innovationfellows
[3] http://ben.balter.com/2015/04/22/the-difference-between-18f-...