My understanding of the situation is that a temporary work permit is acceptable to the Airlines. All they ask is can you legaly work in the USA. I was recently hired by a regional here after being laid off from another regional and my sim partner was from Europe also, He was married to an American and did not have his permanent resident card. It was not an issue for him. All he had to do was go through the TSA Screening to get clearance to start training. Hope this helps. I was lucky enough to get a green card in the lottery scheme(i'm from Ireland) but still had to do the TSA screening.