Can I be fired if I refuse, or do I have some sort of recourse
Please repost your question. It seems to have been cut off. I cannot help you without knowing what the employer is requiring to do.
Wrongful Termination Lawyer
Unless your employer is requiring you to do something that violates a law, rule or regulation, it is unlikely that you would have legal recourse if you were fired for refusing to do it. However, if you would describe what it is that the employer is requiring all employees to do, I may be able to provide a more specific answer or suggestion.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.