It depends on the state. Some have successfully been able to mandate. Others have lost. If it were to make its way to Supreme Court it probably would be ruled unconstitutional to for the government to mandate any medication against a person's will. Roe v Wade guarantees body autonomy as a constitutional right. Everyone remembers the abortion aspect of the ruling but it was really about body autonomy being a constitutional right that cannot be infringed by the government. But it will probably also be ruled that a private entity such as a company can fire or higher based on vaccines. And that the government can probably do the same but it has no legal authority to force someone to get vaccinated with the threat of jail time or fine if they don't.