There is no TP "president", no "treasurer", no "communications director". In fact, the movement is a collection of hundreds, if not thousands of local TPs which identify with the movement as a whole.
I'm intrigued. While I'm sure there's parallels between other organizational entities - revolutionary cells, for one, come to mind - there's a long history of independent Baptist churches in the US that have the same sort of loose structure. You can probably draw some correlations between the Tea Party organization and the decentralized "organization" of the internet, as well... probably more so, in that the TP organization seems to be based more or less on modern social networking and communication mediums.
Some blog, or blogs, out there right now are on their way to becoming the Tea Party version of The Federalist Papers.