KingAir. I don't know about social security numbers but I am heading to San Francisco in January to go to a flight school there and they tell me that you have to have a greencard to work for a US airline.
You must be a citizen and they rarely sponsor foreign nationals although I have met a few people online who have been sponsored.
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"eagles may soar but weasils don't get sucked into jet engines..."
http://users.hunterlink.net.au/~dfckm/weasil.htm