Couldn't you pick a number over the top and have them bring you down? Or are the recruiters likely to not even consider you if you do that?
I based my remark on the knowledge that the range of H1B salaries covered everything from new grad to very senior positions. New grads are nearly all going to fall into the low end of the range at a company like MS, and there's no point in trying to negotiate into a higher pay grade until you've got experience.
Nb - this may be different for engineering; I work in an unrelated field.