OK, time to set the record straight on one or two items.
Firstly, your biggest problem will be immigration. The hurdle here is obtaining your green card.
Secondly, be aware that US law strictly prohibts US companies from discriminating against people who are legally allowed to work in the US. There are a couple of airlines that have tried to make it a US Citizen only profession recently, but have failed miserably. However the airlines do generally restrict employment to US citizens and permanent residents (green card holders). They get away with it because of the requirement to travel internationally, which would be a nightmare for non-immigrant workers.
Thirdly, more extensive background checking is required of non-US citizens which is a hassle and its usefulness is very questionable for many reasons that I will not go into right now. Nonetheless, airlines are hiring non-citizens, although the hiring process is taking a month or two longer for non-US citizens.
Fourthly, there are several regional US airlines that are hiring right now, however it is crucial to understand that most minimum requirements are 1500 total time and 500 multi-engine. Having your FAA ATP is a must to be competitive at most places.
Hope this clears up the details for those of you interested. For credibility's sake, I am a dual UK/US citizen currently in new hire training for a regional US airline.
Ray