Is it possible for employees to sue their employers for violating the Constitution and forcing vaccine mandates, on Employees now that the mandate has

The question

My company had put out a notice of termination if any employee did not receive the vaccine for Covid by October 31. This clearly goes against the constitution and now that the vaccine mandate has been put on hold. Hi happened to be one of the employees that was hesitant to receiving the vaccine but due to threat of losing my job I was forced to receive the Moderna vaccine in order to keep my job and position with the company. The company I work is a private company and did not fall under the presidents vaccine mandates which stated that only medical and government employees are mandated to receive the vaccine by October 31 or face termination. My company has clearly violated the my constitutional right by forcing me to get the vaccine.