Ok, if you don't have the right to work in the US it would be illegal to hire you. You get this right by being a citizen, holding a green card or an H1 visa.
Dug up a listing of H1s (actually the employer's labor certification) for 2010. Twenty six companys in scheduled air transportation made 111 applications. I did not see a single pilot. One crew scheduler, one avionics tech, Iberia brought a station manager in and the others were computer or financial geeks.