How does the First Amendment apply to the employment of a government employee?

The key to the First Amendment analysis of government employment decisions... is this: The government's interest in achieving its goals as effectively and efficiently as possible is elevated from a relatively subordinate interest when it acts as sovereign to a significant one when it acts as employer. The government cannot restrict the speech of the public at large just in the name of efficiency. But where the government is employing someone for the very purpose of effectively achieving its goals, such restrictions may well be appropriate.

Waters v. Churchill, 511 U.S. 661, 675, 114 S.Ct. 1878, 128 L.Ed.2d 686 (1994) (plurality).