Article IV, Section 4 of the Constitution:
"The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion"
The solution:
No, it's not politically possible, today.
But by the time January 2015 rolls around there may be so many additional revelations, that a Republican-controlled Senate, and just enough democrats who wish to save their political hides, may come around.
Particularly if a growing number of Americans demand it.