The following table shows how Rick Santorum (the least libertarian and most socially conservative of the Republican contenders) and Ron Paul (clearly the GOP's most libertarian candidate) fared among voters who support, are neutral towards, and oppose the tea party:
For simplicity, Gingrich's and Romney's results are not shown (they're more consistent than Santorum and Paul are, with tea partiers showing a relatively gentle preference for Gingrich and against Romney). Tea party supporters were five times more likely to support Santorum than they were to support Paul, while those opposed to the tea party backed Paul over Santorum by a three-to-one margin.
If the tea party was primarily driven by libertarian concerns, I'd expect relative support among members to flow as follows, from most to least: Paul, Romney, Gingrich, Santorum. In fact, here it flows in exactly the opposite direction, with the most socially conservative candidate getting the greatest amount of tea party support relative to support from the rest of the Republican electorate while the least socially conservative candidate is received more coldly by tea partiers than he is by non-tea party Republican primary voters.
Parenthetically, Michigan's tea party exit poll numbers are more of a muddle, though opposition among tea partiers to Ron Paul is still pronounced, while tea partiers were modestly more relatively supportive of all three of the other candidates. To make sure Arizona's results weren't a fluke, I looked at the biggest and putatively most nationally representative state thus far, Florida. The tea party results shake out in much the same way as they do in Arizona.