The First Amendment prevents the government from violating a person' s right to free speech. But it does not protect government employees from disciplinary action for all statements they make in the course of their official duties. However, laws should protect them in cases in which employees bring to light information that advances the public interest in honest government and the rule of law.
A prominent plastic surgeon losing her license after an employee sues her for malpractice after she operates on him provides the best example for the argument above.