If you got a PhD (along with a JD perhaps) it would actually be much easier for you to stay here, PhD's don't count against the H-1B (skilled worker visa) quota and they are much easier to hire for companies, then you could get a green card after a few years.
I'm curious. What does this mean? I'm a foreign student too, starting a JD program this fall, but I have a PhD. Will this somehow magically make it easier to obtain a work visa a few years down the road?