Foreign pilots flying for US carriers
Effee:
Your biggest hurdle is getting the right to work (green card). Once that is done, you have just as much right as the next person to get a job you apply for, if qualified. Employers in the US cannot deny you a job because of citizenship, they know that.
Sponsorship for aviation jobs doesn't happen here. There are lots of pilots and company's don't want to bother with that.
I work for a very small airline and about 10% of the pilots here have green cards, and close to a third are naturalized like me. There are foreign pilots flying for jetblue, usair, united, american. I would guess all are applying for naturalization when eligible, but they had green cards and worked as airline pilots.
The US isn't like many other countries in which you have to be a national or just work under contract. That is illegal here.