Can employer not give employees time off when vacation time is requested. We well work over time sometimes. And are getting burned out, we employees work in a long term care facility. Sometimes we work earlier hours staying later after our scheduled shift ends to help with the next shift who happens to be shortstaffed. That is the reason our employer is giving us so we aren't granted our requested time off. Can they do this, is this legal.

Depends on what the stated vacation policy is. An employer is not required to offer paid time off at all. No federal law says they do. Since you neglected to tel us where this is, we can't cite state laws.

Even if there is a policy for vacation time, the employer can refuse to honor requests if staffing needs require. But once a request is granted they can't take it back.