One other problem (in addition to the visa issue) you might have is that some US Government jobs require you to be a US citizen. Mainly those which have security implications attached to them, i.e. DoD, NASA etc. I doubt the FAA comes under that, but then again, you never know. Some airports have dual civil/military use too.
Some towers are contracted out as "Non Federal Control Towers". Sometimes they are paid for by the local City or maybe owned and operated by a third party FAA contractor.
I believe the pay and conditions are often better than regular government paid employees (which isn't that bad either).
Good luck.