No, but this is a common misconception. The First Amendment, like the rest of the Constitution, protects all of us from government infringement on our rights; it doesn't apply to private companies. Some other laws may protect you from being fired for blogging, such as state laws that prohibit employers from discriminating based on an employee's political views or taking action against an employee based on legal, off-duty conduct. For more information, see Nolo's article Fired for Blogging.