The Eleventh Amendment

"The Judicial power of the United States shall not be construed to extend to any suit in law or equity, commenced or prosecuted against or of the United States by Citizens of another State, or by Citizens or Subjects of any Foreign State."

Citizens of any state or foreign country cannot sue a state in federal court without the consent of the state concerned. 

http://gladstone.uoregon.edu/~uofla/Summer00/Tauber.html

I learned that the need for protection against states being sued in the courts of another state was not discussed by the Founding Fathers at all, but rose in 1795 in response to the court case Chisholm v. Georgia. This article goes into detail about a loophole found regarding Amendment 11, Nevada v. Hall.

This video sums up the history of the 11th Amendment in a clear and concise way. To answer the question "Can you sue the government?" You must first answer the question "Did a government official do something unconstitutional? If yes, you can sue and the person may lose their sovereign immunity, although you may never sue a state for money.