"Lindsey GrahamLindsey GrahamOvernight Cybersecurity: Retired general picked to head DHS | Graham vows to probe Russian election interference Overnight Tech: AT&T, Time Warner CEOs defend merger before Congress | More tech execs join Trump team | Republican details path to undoing net neutrality Overnight Finance: Trump blasts Carrier's union leader | What's in the spending bill | Jamie Dimon gets perch for Trump era | AT&T, Time Warner execs grilled MORE has not fared well on our scorecards," he said on Thursday, citing the senator's positions against Club for Growth-endorsed free-market policies.

But Chocola said its involvement in that race is still uncertain because he doesn't know what the rest of the electoral landscape will look like, and that the Club's engagement there "all depends on what the alternative is."

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If the Club does ultimately decide to engage in the race, however, it could make an impact, as seen from its involvement in the Republican primary in Indiana, in particular. There, the group helped force incumbent Sen. Dick Lugar out of the race in favor of further-right candidate Richard Mourdock.

Chocola said, however, that the group will be spending where it knows it can affect the makeup of the Republican Party, to bring more free-market-friendly lawmakers to Congress. That explains its involvement in races considered likely wins for Republicans, like Arizona, where the group spent more than $1 million in the primary to boost eventual Republican nominee Rep. Jeff FlakeJeff FlakeGraham, Durbin 'encouraged' by Trump's comments on Dreamers Unlike Romney, Evan McMullin stands tall against Trump Cures bill clears first Senate hurdle MORE.

“Our first focus is open, safe Republican seats. Our second focus is incumbents behaving badly,” Chocola explained. “Regardless of whether you win or lose, you scare the heck out of the rest of them.”

Graham's campaign pushed back against Chocola's comments with a statement from campaign spokesman Scott Farmer explaining his position on Chinese currency manipulation and the Export-Import Bank.

Though the Club for Growth believes lawmakers should refrain from trying to crack down on China, and opposes the Ex-Im Bank, the statement from the Graham campaign defended his efforts on China and his vote to reauthorize the Ex-Im bank.

“Senator Graham is currently focused on the massive fiscal problems facing our nation and ensuring the United States remains a strong national security voice in a deteriorating world.  He continues to work with the Romney campaign to unseat President Obama, and he's campaigning hard to win a GOP majority in the Senate. But come 2014, our campaign will highlight and run aggressively on Senator Graham's distinguished conservative record that reflects South Carolina values," the statement reads.

--This story was published at 11:11 a.m. and updated at 4:18 p.m.