Not in a primary system. The Tea Party crowd, while not in love with the Republican Party, show no signs of becoming a third party to run candidates against the 2 parties. I know there are exceptions (Nevada), but the tea party leaders such as Palin have talked about re-making the GOP. Conservative talk radio has discouraged the formulation of a third party also.
A good test of this theory will be Florida's Senate race. Rubio has overtaken Crist and Crist may run as an Independent, even though he took GOP money and pledged to run as a Republican. I still believe Rubio will win that race.
It is amusing to me to see the left portray the Tea Party as racist, dumb, astroturf, right-wing nutjobs, and now fractured. I don't see Obama stopping his leftist agenda anytime soon which serves to fuel the Tea Partiers' discontent.