Bill Frezza writes in Forbes "Why The Tea Party Should Endorse Gay Marriage":
Why gay marriage? Aside from being a live-and-let-live litmus test (what part of get the government out of our lives don't you understand?), gay marriage is the perfect pivot issue. Coming out in favor of granting same-sex couples the same legal status as heterosexual partners can shatter the negative stereotypes pinned on the Tea Party while having no impact whatsoever on anything that really matters to anyone, unless you happen to be gay.
Selling gay marriage to the tea party is going to be tough, considering that the Pew Research Center found that only 1/4th of self-identified Tea Party people support redefining marriage (other sources claim an even lower level of support).
Ideologically, it would seem that Tea Party people are more prone to see gay marriage as government intervention in people's lives (considering that every popular vote in 31 states has supported marriage, and only liberal legislatures and judges have seen fit to impose SSM).
As for supporting same-sex marriage as a way to "shatter negative stereotypes", one of the defining characteristics of the Tea Party is a distinct disregard for what liberal elites think about them.
And as for "having no impact whatsoever on anything that really matters." The family, traditional values and respect for our Constitution all really matter to Tea Party people.