Four years after Atlanta saw some of the earliest and biggest tea party rallies in the country, Georgia’s GOP establishment, including Gov. Nathan Deal, are pondering strategies to reduce the right-wing insurgency’s influence on next year’s primary election for a US Senate seat – and on the larger struggle for power in Washington.

To be sure, Georgia is about as red a state as they come. It has had an all-Republican contingent in the US Senate for years, and the state gave a big thumbs-down to Barack Obama twice.

But the emergence of a big-name Democrat – Michelle Nunn, daughter of longtime and big-time former Sen. Sam Nunn – suddenly has the state GOP on the defensive.

As mainstream GOP leaders see it, the problem is how to keep the state’s powerful tea party contingent from dominating the primary nomination process and picking an extreme-right candidate who couldn’t win a general election.

Moreover, to win control of the US Senate, Republicans must reel in six seats in 2014, and that means not losing seats presumed to be solidly in their column, as they did in 2012.

The national GOP establishment is still smarting over losses in Missouri and Indiana that not only helped deny Republicans their Senate majority but also put new dents in an already dinged-up GOP brand. Missouri’s 2012 Senate GOP primary winner, Todd Akin, set off a furor with his comment that victims of “legitimate rape” seldom get pregnant. In Indiana, tea party favorite Richard Mourdock doubled down on that gaffe by suggesting that a pregnancy resulting from rape was “something that God intended to happen.”

Though Ms. Nunn has never been elected before – she’s a longtime executive of nonprofit groups, including at one point heading former President George H.W. Bush’s Points of Light Foundation – her candidacy has energized Democrats, many of whom believe she could win a matchup against arch-conservative Republican candidates such as US Reps. Paul Broun of Athens, Ga., or Phil Gingrey of Marietta, Ga., both of whom politicos say have extreme fiscal or social views that are likely to alienate general election voters.

Congressman Broun (pronounced “Brown”), a physician, has become known nationally for a YouTube video of a speech, filmed before a wall of stuffed animal trophies, in which he denounces the theory of evolution, calling it a lie “from the pit of hell.”

“God’s word is true,” said Mr. Broun in the video. “I’ve come to understand that. All that stuff I was taught about evolution, embryology, big bang theory – all that is lies straight from the pit of hell. It’s lies to try to keep me and all the folks who are taught that from understanding that they need a savior.”

Representative Gingrey skidded into a similar red zone for general election voters when he referred to Congressman Akin’s comments on rape as “partly right.”

“There really is a battle going on, and they’re all conservatives, but it’s a question of, ‘What kind of conservative are you?’ ” says Alan Abramowitz, a political scientist at Emory University, in Atlanta. “It’s less about issues than it is about rhetoric and tone and emphasis.”

With seven GOP candidates already in the Senate race, a strong showing by a far-right-wing candidate in the primary would likely lead to a runoff against a more establishment Republican candidate. With low turnout, most bets are off as to the outcome.

One political fix, floated last week at a meeting among Governor Deal, Secretary of State Brian Kemp, and House Speaker David Ralston, is to hold the primary in late May, during pre-vacation season, rather than during the dog days of summer, in a bid to increase turnout. Speaker Ralston and Lt. Gov. Casey Cagle both threw their support behind such a bill this week. Deal says he'll leave it to the legislature to make the change.

“Historically, primaries in Georgia have been conducted … during the dog days when many families check out of their daily routines,” writes Jim Galloway, a longtime political columnist for the Atlanta Journal-Constitution.

He then explains the reasoning behind the idea: “A pre-Memorial Day primarily would ensure a larger GOP turnout with a voting population more akin to a November general election, and less likely to be dominated by the GOP’s most fervent and conservative activists.”

Many in the national GOP establishment believe the party, to succeed nationally in the short and long terms, needs to move toward the center on issues such as immigration in order to appeal to more people, including Hispanics and younger voters.

But hard election evidence suggests that mainstream Republican ideas, including compromise on immigration reform, “seem to be going against the views of most Republican primary voters,” says Mr. Abramowitz at Emory.

The handwringing and machinations in Georgia mark an increasingly bitter civil war in Republican ranks, fought out not by politicians out to change the rules of political competition, but also by a vast fundraising establishment that picks winners and losers before a single vote is cast.

Club for Growth, which funnels money and support to fiscally conservative Republican candidates, has not made an endorsement yet in the Georgia primary, but Broun ranks No. 1 on its legislative scorecord, with a lifetime score of 100 percent.

Club for Growth spokesman Barney Keller challenges the political theory that the so-called extremists are dashing GOP election prospects.

While Akin and Mourdock both lost in states with long Democratic traditions, and more because of major gaffes than policy positions, moderate Republicans in red, purple, and blue states also lost, including Linda Lingle in Hawaii, Rick Berg in North Dakota (a state won handily by Mitt Romney), and former Gov. Tommy Thompson in Wisconsin, he says.

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“When candidates run who can clearly articulate a fiscally conservative vision for the country, and can explain their pro-growth principles to voters, they can win even in blue states like Pennsylvania, purple states like Florida, and even in tough races in states like Arizona,” where Jeff Flake prevailed in 2012 against Democrat Richard Carmona in a very competitive Senate race, he says.

That analysis is supported at least in part by a July 31, 2013, Pew Poll that asked rank-and-file Republicans directly what the party should change. Fifty-four percent said they believe the party needs to become more conservative, not less, to win. Forty percent said they would like to see the Republican Party become more moderate in tone and policy.