Washington Post reporter Ben Pershing gives the Tea Party movement and Ron Paul too much credit:
Ben Pershing: So far Ron Paul has given no indication that he wants to form a third party. If he did, it would have a pretty obvious name -- the Libertarian Party. Unlike the Tea Party groups, which combine elements from a variety of different ideologies (and also have plenty of disagreements amongst themselves), Paul has a long-developed and clear Libertarian philosophy. But he hasn't done anything to suggest he wants to form a third party rather than just try to move the GOP in his direction. Note that's what his son, Rand Paul, is doing in the Kentucky Senate primary.
First, I'm not sure how many different ideologies are actually represented by "the Tea Party groups." There's conservatism, and some libertarianism. What else? Liberalism? No, not really. (Worth keeping in mind: Tea Party folks are very, very Republican.) Socialism? Anarchism?
Second: Ron Paul's "clear Libertarian philosophy" doesn't include abortion. He opposes abortion rights. The Libertarian Party (like Ayn Rand, among other libertarian heros) says "we believe that government should be kept out of the matter." And Paul calls the Defense of Marriage Act "proper," while the Libertarian Party platform says "Consenting adults should be free to choose their own sexual practices and personal relationships. Government does not have the authority to define, license or restrict personal relationships." So, basically, Paul's "clear Libertarian philosophy" is that he opposes government intervention in people's lives -- except when he supports it.