You have to differentiate between party heads and supporters. Among supporters of any party are all kind of cooks, who happen to think that the particular party will get their issues resolved. I don't know much about tea partiers, because I don't live in the US and never have except for a brief 4 month period, but I'll draw a parallel with a situation I do know:
A certain party that is economically conservative, anti-corruption, and socially liberal is being flambasted by mainstream media for being populist, ultra-conservative, and destructive. It's a long discussion on why it is so, but you'll have to trust me on this, because my point is what follows. Because this party was marginalized by mainstream media and mainstream politicians and big business (hint: they really are anti-corruption), the marginalized elements of society who are indeed ultraconservative socially and feel marginalized ended up being the strongest supporters of this party as a social group. These ultracons really are quite dumb, but they have noone else to vote for and they really want to vote for someone, because they're undeniably patriotic.
My evidence for the party being socially liberal is that when it was in power and could easily ban all types of abortion (as its ultra-conservative constituent would like), it did not. And it did this to such an extent that it tolerated a number of MPs leaving the party to form a new socially ultraconservative party based on this abortion issue alone. My conclusion on this is that when media manipulate the image a political movement wants to project, they end up recruiting for that movement a group of people who identify with the marginal viewpoints while deterring the ones who really should be supporting the movement. This actually mutates the movement and renders it sterile. It's sad, but mainstream politics and media probably know very well that they are doing this and they will continue to do it.
If you want some hints on where I have my example from, I'll tell you that the current party leader's brother died in a plane crash while serving as president of the country.