Can I be fired for my Facebook posts?
Most likely, yes.

The legal landscape is littered with appellate court decisions upholding employers' right to fire employees for posting offensive material on Facebook.

First, consider whether a 1st amendment free speech issue is involved. This is easy. The 1st amendment applies only to the government (federal, state, local). So if the employer is a private company, there simply is no 1st amendment protection for the employee.

When the government is the employer, the employee might get some protection if the posting deals with "a matter of public concern." This is something more than a personal "gripe," and is pretty easy for the employee to demonstrate.

Then the court is going to go through what is called the Pickering balancing test, named after the 1968 US Supreme Court case Pickering v. Board of Education. As the Court put it, "The problem in any case is to arrive at a balance between the interests of the [employee], as a citizen, in commenting upon matters of public concern and the interest of the State, as an employer, in promoting the efficiency of the public services it performs through its employees."

Just this week the 7th Circuit decided Hicks v. Illinois Department of Corrections [PDF], upholding the suspension of a corrections sergeant who posted Islamophobic and offensive material on Facebook. The court had no trouble showing how this was in opposition to the goals of his employer and resulted in an adverse news article.

Your results may vary. If you have this issue, consult a good employment lawyer.
(Not me, I'm an arbitrator.)