It's still oddly common to hear the Tea Party characterized as a libertarian movement, but libertarians are not the same as Republicans, whereas the Tea Party differs materially from Republicans on exactly nothing, as I explored a few months ago. The pig-headed denial of climate science is a more recent illustration.
Each of the victorious Tea Party Senators -- Pat Toomey, Rand Paul, Marco Rubio, Ron Johnson, and Mike Lee -- support criminalizing abortion,oppose legalizing same-sex marriage, and otherwise march in lockstep along with the usual far-right culture war preoccupations. Tea Party electoral losers like Sharron Angle, Joe Miller, and that not-a-witch who tried for Senate in Delaware are, if anything, even more at home with religious right lunacy and correspondingly less at home with actual libertarian thinking (such as it is).
Even the GOP's house organ can't gin up any convincing differences between Tea Partiers and garden-variety Republicans, so they focus on rhetoric:
Tea Partiers want to balance the budget, end runaway government spending, including pet projects for lawmakers known as "pork," and stop the tax hikes.This implies, or seems to try to imply, that Republicans are constrained by their own actions from railing against "big government" and wailing for ever more tax cuts, but of course nothing is more common than for a Republican to bleat about the same "excessive spending" and "runaway deficits" they advocate when in front of select audiences.
While Republicans aren't opposed to those demands, they have come under fire for running up the deficit when they were in power, including the $700 billion Medicare prescription drug benefit that wasn't paid for and initiating the bailout of Wall Street and the auto industry after the 2008 economic collapse. [emphasis mine]
The Tea Party is a temporary placekeeper for Republicans who want to seem to pretend to be independent of the Republican party. Now that many of them are in office, they will do exactly what Republicans always do -- increase deficits while whining about deficits.
The Tea Party is the GOP. The GOP is the Tea Party. They're the same.