As far as I have understood………When a company hire a candidate, they do not expect the candidate to know everything and they basically hire employee and train them (I.E the employee will be working under supervision). Then after the period of 2-3 years the company will get more out of this employee because he would have learned most of the things he needs to for his field. But In case of international student it's not certain that the employee will be working for that company in next 5 years. Until and unless you have a Green Card it's hard to find JOB. 

Try your luck with some private company. If the company you are applying has some link with the federal government…..(Meaning…if the company is under federal contract or the company works as the contractor of the federal government ) than the company wont hire you because it's illegal to hire you due to the executive order issued by the BUSH Administration in 2002( Which is active till today). But, Private company may take a chance and hire you even if you don't have green card provided that they are not under federal contractor. 

I am also doing Mechanical and Aerospace Engineering and I too don't have Green Card but my career service officer in the University told me that it would be hard but not impossible to find the job in my filed. The Career path website of my university has many job posting where the requirement is F1, Greencard or US Citizen. I am not scheduled to graduate until 2011 fall.