COLUMBIA -- Cracks in Republican support for GOP gubernatorial nominee Nikki Haley surfaced for the first time Thursday.

What Haley does in the next month to respond is critically important.

Socially conservative Republican leader Cyndi Mosteller of Charleston and GOP strategist and Clemson University professor Dave Woodard came forth publicly to demand answers from Haley.

Specifically, they said they want her to speak up about allegations that she was unfaithful to her husband, along with addressing ethical questions about her job at the Lexington Medical Center Foundation and her late payment of income taxes.

They said Haley has dodged the issues too long and that it could come back to hurt the party.

"Truth is always good politics," Woodard said. "Nikki wants votes. We want answers."

Their comments have done something to push back against Haley's campaign that Democrats haven't been able to do: bring the extramarital allegations and Haley's dirty laundry to the forefront again. She faces Democrat Vincent Sheheen on Nov. 2. Sheheen's campaign did not immediately react.

But state Republican Party Chairwoman Karen Floyd and former state party Chairman Katon Dawson said the issues have been put to rest by Haley.

"The status quo is scared and it's simply lashing back," Floyd said. She took the microphone after Mosteller and Woodard's news conference in the Statehouse lobby, flanked by Republican representatives from the tri-county area, among others conservatives.

Floyd called the pair's public comments "deplorable," and she repeatedly stressed that the party is strong and united.

Longtime political analyst Neal Thigpen, a retired professor, said he can't exactly figure out what to make of the dueling news conferences. "The only thing I can say is the Mosteller-Dave Woodard axis is the only discord from anybody who approaches establishment Republicanism," Thigpen said. "Around Florence, all these big-dog establishment Republicans, who are the big money people, they are standing at the door with their checks in the hand."

Those supporters expect Haley to win in November, and they want to be assured that they have access to her in the governor's mansion and can hold on to their own political appointments, Thigpen said.

Charleston Democratic Sen. Robert Ford said he's heard whispers from Republican friends who want Sheheen to replace outgoing Gov. Mark Sanford. But Ford said they're too afraid to go public for fear of backlash.

Woodard said he, too, sees the writing on the wall. With Haley pulling a double-digit lead in the polls, he expects her to topple Sheheen. But Woodard said he felt his concerns about her character were too significant to dismiss.

Rob Godfrey, Haley's campaign spokesman, said the Republican leadership's show of force is telling. "Nikki is grateful for the overwhelming support she received in the Republican primary, and the even more overwhelming support she enjoys from Republicans, Independents and Democrats today," Godfrey said in an e-mail Thursday. "Everyone is entitled to their own political agenda and their own free speech, and you just heard some of that today."

Haley did not respond directly.

Mosteller said she and Woodard are establishing a group to push for answers called "Conservatives for truth in politics." Woodard said the group will pay to run ads if it gets enough cash to do so. The group is made up of about 25 people, Mosteller said, and will not endorse or oppose any candidate.

"It's now time we hear directly from (Mrs.) Haley," Mosteller said. "She wants our vote, our sacred vote. We want to know that she has earned our sacred trust."

In recent weeks and months, media outlets have investigated Haley's tax records and her job at the Lexington Medical Center Foundation as well as allegations that she had affairs with two different men.

Haley vehemently denied the alleged affairs. Her campaign produced e-mail records for review in their headquarters, but Mosteller said the records weren't complete.

Reviews of Haley's tax records have shown that she has been fined for repeatedly paying her personal and family business' income taxes late.

With regard to the controversy surrounding Haley's job at the medical foundation, The State newspaper reported earlier this week that a more-than-$100,000 fundraising job was created expressly for Haley.