I had a similar question a couple weeks ago. From what I understood by searching this forum, we wouldn't be able get sponsors but I may be wrong.
I know a friend of mine is being sponsored by one of the big four accounting firms.
He came to the US with a student visa and right now he lives in California and supposedly will have his status fixed due to the job opportunity.
My question was that since he had a student visa and we may have a work permit, how would it not be possible for us to be sponsored?