South Carolina state Sen. Lee Bright (R) is "leaning towards" mounting a primary challenge against Sen. Lindsey GrahamLindsey GrahamGraham: I'm still not supporting Trump North Korean official calls Trump idea of meeting 'nonsense' The Hill's 12:30 Report MORE (R-S.C.), he told The Hill Monday afternoon.
Bright criticized Graham's fiscal record as well as his views on climate change and immigration.
"We've got a real battle for the heart and soul of the Republican Party right now and he's on the other side of the battle," he said.
Graham has had a target on his back from some conservative groups because he has worked towards bipartisan compromise on a range of issues, but no candidate until now had stepped up as a likely opponent.
South Carolina state Sen. Tom Davis (R), another Tea Party favorite who told The Hill late last year he was unlikely to run against Graham, officially ruled out a bid last week.
Bright said he'd been talking for some time with the fiscally conservative, well-financed Club for Growth, which often backs conservative insurgents to Republican incumbents in primaries and has been critical of Graham in the past. He said he has a perfect lifetime score from the group and hopes to secure their backing.
"I've talked with them a little bit privately in the last few months. Now it's going to get a lot more serious," he said.
Club for Growth Spokesman Barney Keller declined to weigh in.
"We're watching the race," Keller said, when asked about the meetings and whether the Club might support Bright if he runs.
Graham is more popular with South Carolina conservatives than those in Washington, D.C., however, and is a proven campaigner and fundraiser. The newly formed super-PAC Conservative Victory Project, which has the support of top GOP strategist Karl Rove and plans to target Republicans they view as too conservative to be electable, could also get involved in the race.
The conservative state senator disputed a Monday report from local political blog FITSnews.com that he had definitely decided to run for the seat. Bright said he didn't "know where that came from" and wanted to make sure he had a path to victory before he fully committed to a race. But he indicated he's likely to run.
"You don't want to run unless you can win. I have a lot of folks encouraging me. I'm starting to have more serious discussions with grassroots people, fundraisers and people around the state," he said.