As an undergrad I read An Economic Theory of Democracy, by Anthony Downs, which gives a nice explanation of the Median Voter Model and it's main thesis that campaigns with two candidates are a race to the middle. Put in a third candidate who is extreme right, who will siphon off some votes of voters with preference near to that extreme, and that alters the Downs prediction in that the location of the other two candidates is no longer the median of the entire population but rather the median of those who continue to vote for the two original candidates. That point will be more leftward than the original median. Reality is not that simple, of course, but it is an intriguing thought.
Candidates who are well known and have historically developed positions on issues may not be quite as flexible in their positions as the Downs model indicates. In this case in an election where the traditional Republican candidate is to the right of the Democratic candidate, the Downs logic would suggest that the the presence of a Tea Party Candidate would hurt the traditional Republican but not the Democratic candidate. One can quite reasonably argue that the voters have multi-dimensional preferences so are unlike what Downs models. And one might also argue that the process is sequential, primary first, then election. So there is no direct three-way competition. But if Tea Party candidates run in the Republican primary and lose there and then decide to run in the general election anyway as a third party candidate, you should get something like the prediction above.
This seems like something worth betting on.