As someone mentioned earlier, a green card is essential to secure a job in the US even if its regional airlines (I have a cousin who works for one so I know).
How long will it take to get in an airline? Depends on your luck. I know a pilot who is on the airbus 320 at the age of 23 and at the same time I also know of another pilot who is enrolled in the same course at the age of 38. Plenty of s/e experience under his belt though.
If you are really on a tight budget, you should consider looking for flying schools in Asia for cost effective training.