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Not at all. Most research schools don't care about citizenship, etc. They want the best. Community colleges might care and even small universities but big research schools definitely want the best.
 
yes, initially for H1b and then for green card.
 
hgd7833 said:
I am PhD student in mathematics. I have publications right now ( 2 articles ) and will extend to 4 or 5 by the end of my study.
I also have twi experience as a university instructor in middle east universities
http://chronicle.com/jobs/0000639251-01
 
I am sure that you have had professors who are from other countries, especially in mathematics I would imagine that you have a lot of professors from Mainland china or India. Large universities have legal departments that specialize in green card processing for academic employees. Right now because the economy is bad, universities have had their funding cut, so there may not be as many jobs available compared to when the economy is good.

If you can prove that you can bring in grant money from your research all the more they are likely to hire you.