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(CNN) -- There's one thing Kentucky Republican Senate candidate Rand Paul and his Democratic opponent Jack Conway have in common: They're both finished talking about "Aqua Buddha."
Conway's controversial attack ad paralyzed both campaigns this week. The spot accuses Paul of once belonging to a group that mocked religion in his college days at Baylor University. The ad features a claim from an anonymous woman who told The Washington Post and GQ magazine that Paul's group forced her to pray to a false idol named Aqua Buddha.
At a news conference at the Atlas Machine and Supply factory outside of Louisville, Kentucky, Paul signed a pledge to repeal the estate tax, dubbed the "death tax" by conservatives. But most of the questions from reporters were focused on the Aqua Buddha controversy.
In a brief interview with CNN, the Tea Party-backed Republican rejected the ad's allegations and slammed Conway for running it. "I think he ought to be ashamed of himself," Paul said. "In my entire life, I've written and said a lot of things. I've never said or written anything un-Christian in my life."
Answering only a few questions, Paul walked away from the interview.
Paul's campaign told CNN on Friday that he will take part in a debate Monday night. He had previously threatened to pull out after Conway raised the Aqua Buddha issue.
Conway also resisted questions about the ad at his own campaign events this week. The Democratic candidate and the state's current attorney general now plans to run more issue-oriented spots in the final days of the campaign, letting the Aqua Buddha ad "run its course." He still defends the commercial. "I'm not questioning Rand Paul's faith. I'm questioning his actions," Conway said.
But some of Conway's own supporters in the state have questioned the wisdom of running the ad. Conway backer and Christian County Judge Executive Steve Tribble told CNN, "I might not have done it." Tribble said he understood why Conway ran the spot, noting Paul has said "some strange things."
A critic of the bank bailouts but a supporter of the new health care law, Conway is running in a state where President Obama is deeply unpopular. He's opted to campaign with former President Bill Clinton instead of Obama. When asked about his reluctance to have the current president at his side, Conway said, "This campaign's about me versus Rand Paul."
Conway's latest line of attack is that Paul once indicated his support for scrapping the income tax, in favor of what conservatives call the "fair tax." It's essentially a 23 percent national sales tax on all purchases. Paul told CNN he's open to the idea but not sold on it.
"I've always said I'll support any tax reform that lowers taxes on everyone. So that's sort of the rule of thumb that would have to be. And that simplifies the tax code. That might be one of the alternatives. So would be a flatter income tax," Paul said.
Paul has granted few national media interviews since he won the Republican primary in Kentucky earlier this year. In the days following that surprise victory, Paul's libertarian views came under scrutiny after he raised questions about the 1964 Civil Rights Act and the Americans with Disabilities Act.
Paul never imagined his behavior in college would be fair game. At his news conference, he said the Aqua Buddha ad would discourage future candidates from running for political office. "Do we want to have a religious test in our country?" he asked.