Can't help you with green (actually white) cards etc. Good luck with TSA (Thousands Standing Around). TSA is just another over-bloated US bureaucracy (like Homeland Security, the CIA, FBI, NSA, Dept. of Justice, Federal Marshals, ATF, Customs and numerous police departments are simply not enough...), which vaguely understands what the real security issues are, but they have gotten a little bit better.
If you can ever get a job with NetJets or such, this might have a fair bit of job security, but with thousands of laid-off US pilots, there might be strong competition. A pilot fortunate enough to get hired might be wise to spend a career there, because they had steady growth and high fuel prices are sinking most passenger airlines into quicksand. One recalled some of its furloughed pilots this winter, and many of these might get laid-off again, when it files for Chapter 11!
Years ago, part of Northwest Airlink, now Pinnacle, had a number of pilots from other countries who were somehow "sponsored", whatever that means. They now pay you nothing during training, and some ladies, maybe even guys with only a few hundred hours, have been hired. It is challenging groundschool training on the CRJ, naturally requiring many pilots' first exposure to an FMS. Most seem to make it through training.
Pinnacle's headquarters might be in College Park, near Atlanta Int'l Airport (ATL), GA.