Yes but your employer can be sued for firing you and can lose.
Good coverage by the NYT on this issue and lawsuit (and a note about reporting such small business items to the NYT reporter who will be covering them):
Editor’s Note: Adriana Gardella will be reporting periodically on legal issues affecting small businesses. If you know of an issue or case that you would like to call to her attention, you can email her at email@example.com.
With the rise of social media, many business owners have sought to control what their employees post on the various social networks. But as the owners of Triple Play Sports Bar and Grille in Watertown, Conn., learned during recent litigation, employers may have less authority than they think.
In August, a three-member panel of the National Labor Relations Board in Washington concluded that Triple Play violated the National Labor Relations Act when it fired two employees over comments made on Facebook about a Triple Play owner. The N.L.R.B. also determined that Triple Play’s written social media policy violated the Labor Relations Act. While the policies of large companies have come under increasing scrutiny, small-business owners are now on notice that they must also be concerned about these policies and how they enforce them.
Ms. Gardella goes on to report the case thoroughly: When Employees Knock Their Bosses on Social Media – NYTimes.com.