The scope of the effect that a third party has in the United States is extremely limited. Not only do candidates from the Tea Party need to outcompete opposing members from the Democratic Party, but they also have to compete with members of the Republican Party, a party with which it shares very similar ideology. In order for third parties to successfully enact their agenda, minor parties like the Tea Party either have to influence the elections of major party candidates that they support, or prevent the elections of candidates they oppose.
It is clearly possible for members of the Tea Party faction to reach positions of power. Several candidates have been elected to the U.S. Congress. These members, however, have run on the Republican ticket,