The Permanet Resident Visa, aka a "green card" because, ah, it's green, will be a requirement. No American airline is going to sponsor a foreign national for a visa with the number of American passport/green card holding pilots available for work. Once past this hurdle, the fact you are a foreign national will be irrelevant.
There's some info in the North American forum. It may be on the "converting JAA to FAA" thread.