Libertarians welcome anyone who opposes the government on any issue, for any reason. The nature of that opposition is irrelevant to the Libertarians. This is the same essential position being taken by the Tea Party movement.
Consider some of ideas on display at the Tea Parties: term limits, "state's rights", and succession are a few. Each is a superficial issue, and in the case of "state's rights" and secession simply asinine. For example, many advocates of "state's rights" are not opposed to violations of individual rights; they simply prefer for those rights to be violated on the state level, rather than the federal level.
Certainly there are also better ideas being expressed as well. Signs referencing Ayn Rand and John Galt are common. Which means, the Tea Party umbrella includes John Galt and George Wallace, advocates of freedom and advocates of statism. Such diametrically different ideas cannot long exist within the same movement.
I am not suggesting that Objectivists boycott the Tea Parties. The movement is too new and ill-defined to know what direction it will ultimately take. I am saying that if it continues its present course, it will ultimately be dominated by the more irrational elements. As Ayn Rand wrote in "The Anatomy of Compromise":
When opposite basic principles are clearly and openly defined, it works to the advantage of the rational side; when they are not clearly defined, but are hidden or evaded, it works to the advantage of the irrational side.
Politics is not a primary--it rests upon the more fundamental branches of philosophy. One's views on the nature of reality (metaphysics), the nature of knowledge (epistemology), and the nature of man (ethics) ultimately shape one's views on politics.
As Peter Schwartz has pointed out, the why determines the what. Why a particular position or view is held determines what it ultimately means. For example, an individual who watches NASCAR for the occasional specular crash "appreciates" the sport for an entirely different reason than the person who enjoys watching man control a precision machine. While both are fans of the same sport, their reasons for watching--the why--give vastly different meanings to their participation--the what.
In the context of politics, ethics provide the "why". One's view of the nature of man, and the actions appropriate to man, determine the meaning of one's political views.
Thus, while the Tea Party participants may hold the right position on many issues--such as limited government and abolishing the Federal Reserve--the reasons they hold these positions will ultimately determine their true meaning. In the absence of a rational morality, the "right" position cannot be defended.
Libertarians have abandoned morality, regarding it as a constraint on their whims. If the Tea Party movement wishes to have relevance, it must discover and embrace the only morality that can defend the right political positions. It must discover the morality which upholds the right of each individual to his own life, liberty, property, and pursuit of happiness. It must discover rational egoism.