The current Republican party is in no way republican. The word "republican" comes from the Latin "res publica" meaning public thing. In the Eighteenth Century Anglo-American world, it meant considering the public good over private gain. In the Twenty-First Century United States too many Republicans consider the private good of large corporations over the public good of a well-governed nation.
So many Republicans do the bidding of ALEC, the American Legislative Exchange Council, and take big bags of campaign donations from the member companies to promote these companies' private gain, I wonder if the Republicans shouldn't be called ALEC's Bag-Time Band.
Fortunately, we do still have a republic with a democratic foundation. Some of the people are getting fed up with a narrow-minded party that many movements have begun to get us back to some semblance of civility and interest in the public good.
There is the Coffee Party that calls for "civility and reason". Although many of its stances might be considered on the left, it is more for people rather than corporations.
It has a "community" called Coffee Party Conservatives: The Conservative Side of the Coffee Party USA, but it is a aggregator of news that generally finds fault with the current Republican Party, though Obama and the Democratic Party do get a bit of criticism.
One of the interesting articles referenced is "A Phoenix Rising: Common-Good Conservatism" by Michael Stafford and D.R. Tucker, Truthout, 2012-04-27. Stafford and Tucker are or were Republicans.
Even a member of the conservative think tank American Enterprise Institute, Norman Ornstein, along with Thomas E. Mann has written a critique of the current Republicans: "It's Even Worse Than It Looks: How The American Constitutional System Collided With The New Politics Of Extremism"
by Thomas E. Mann and Norman J. Ornstein. You can listen to an interview of them on NPR and read a summary of the interview at "Extremism In Congress: 'Even Worse Than It Looks'?", 2012-04-30.