If you refuse the H1N1 vaccine from your employer and you contract H1N1 what can your employer do to you?

I doubt that any court has ruled on a case like this yet, and it's quite a bit off the beaten track, so there's no way to be sure.  If your work has anything to do with providing health care services or food preparation or processing, that might affect the result in the employer's favor.

I'm assuming you're an employee "at will," with no written contract between you and the company.  So, under the law, they don't need a reason to fire you.  However, it's possible that if you could show that getting the flu is the "real" reason you were fired, it might be wrongful discharge under the Americans With Disabilities Act ("ADA").

Your employer can't control what the insurance does or does not pay;  you should still be covered for the illness.  Whether you have the legal right to sick leave would depend on what you can prove about your company's policy on that.