It is legally possible to force the US government to do things against its will, for example look into a Freedom of Information Act request.  They are also legally obligated to do certain things under certain circumstances, for example keeping juvenile criminal records from becoming public.  It is more an example of the second type I was looking for: some existing method I could use to send them a key they were then obligated to keep, and keep privately.

And Seriouscoin?  You need to get out more...