Clarification on the legal issues in whether or not an organization can claim tax-free status comes in this article by Joe Klein of Time. In brief, political organizations cannot make this claim, policy advocacy organizations can.
Many of the so-called "tea party" organizations engaged in quite a bit of both policy and politics, I suspect. If this article's explanation is accurate and legally binding, the situation is much more complicated and less clear-cut than at first blush.
