The thing about the Tea Party to remember is that it is decentralized. There is no Home Office or franchise system to ensure that each chapter holds identical ideals in the same priorities. A Tea Party chapter in Wisconsin or Michigan might have different beliefs in union relations, or pursue them with a different intensity, than a chapter from, say, Mississippi or Georgia, who might focus more on gun control. This example is by region, but they vary in plenty of other different ways as well, so you can't hold them to hard and fast mission statements.
The other thing about them is that they're vulnerable to being co-opted by special interests. The existence of Super-PAC's means completely untraceable money, which makes it super easy for crafty political operatives (who are much better at doing these sorts of things, than any of us are at spotting them) can and do bend a movement like the Tea Party to whatever they want - most likely, lining their own pockets. The other place where we saw this happen was the quick flare-gun life span of the Occupy Movement, who got co-opted by every union, left-wing think tank, and iced tea dispensary with staggering speed and efficiency.
So any analysis of the Tea Party has to be done in generalizations, and with a certain amount of cynicism. As best I can figure, the main feature that most of the Tea Party rallies around is lower taxes, both personal and (by some) corporate. That, and the logically-following austerity, are clearly Republican ideals; modern Democrats are more likely to "tax and spend", promoting entitlements, welfare, infrastructure, and so on, while understand that (to paraphrase Clinton) some 'sacrifice' will be necessary.
As for the other tenets, most of them skew Republican as well. Look at the items on that list of 15 that voters are most passionate about. Abortion is (wisely) avoided completely, but the phrasing of their stance on immigration, gun control, family values (that is, gay rights), and lowering taxes all take the conservative side. I don't believe anything there is solely the view of the left.
Face it: The Tea Party is a Republican- and right-leaning movement. It's not unusual, though, for Tea Party darlings to try and convince left-leaners that it appeals to them as well, even though in most spheres it really doesn't. That's Recruitment 101.