Though this is a bit opinion based (as only any talk of where center is can be)... the Republican Party is already right of "center". It's all relative of course - the US Democratic party would most likely be Centre-Right in most other places.
This is kind of like the joke about morals. "Im perfectly moral, anyone looser is a slut, anyone tighter is a prude, i just happen to be perfect". Both parties like to claim the Center, to be "real America". Forget center, lets worry about relative - Republicans are (almost always) Right of Democrats, and Tea Party Republicans father Right still.
The Tea-Party wing isn't, by political science terms, "conservative". The proper term is Reactionary. They are moving from Right to much Farther Right. Conservative says "lets stay where we are". The Tea-Party is more "Lets go back to where we were before."
The Gold Standard? Generally accepted as unworkable during The Great Depression. It's cool in good times, causes horrible horrible spirals in bad times. Most countries moved off of it in the 1930's. We started then, and moved completely off in the 70's, Tea Partiers want to go back to that. The fact that the locked exchange rates of the Euro countries, which act as a mini-gold-standard, exacerbated and deepened a crisis there notwithstanding.
The New Deal? Trying to rollback a lot of it (though Republicans in general want to also).
Voting Rights? Attempted rollbacks. Though the rollbacks tend to hit minorities and poor people (who don't tend to vote Republican) more.
They claim to want to go back to the Constitution. Where women couldn't vote? Where a black man was defined as 3/5 of a white man? Very Reactionary. I'm in Chicago, which wasn't in the Union in 1783. Maybe as a Tea Party person, I'd really need to talk to the Algonquin Indian tribe for leadership. I'll make sure to find some nice French Canadians to trade furs with.
We live in a complex world. A lot of people want to pretend the complexity is just a screen, that it's a cloud inflicted by (assumed to be evil) men and that they can see the Truth, the Simplicity. These are the people who are voting Tea Party. Are they batshit? Dunno. But the world is complex. And if your model of the world is to ignore the complexity and pretend it's simple, you're going to want to pull the wrong levers, and you'll most likely cause some damage.