Herman Cain Faces Reporters on Live TV and Agrees to Lie Detector Test (Video)

Herman Cain - Romney And Cain Address Defending American Dream - h - 2011
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UPDATED: The presidential candidate calls Gloria Allred's client a "troubled woman" whom he does not even know, and repeats that sexual harassment accusations are "baseless."

Herman Cain faced reporters in Phoenix, Arizona during a televised press conference and told a CBS reporter that he'd take a lie detector test to prove that four women -- or five, depending on which reports you deem credible --  lied when they accused him of sexual harassment.

"As distasteful as it might be, would you be willing to do a lie detector test?" the CBS reporter asked.

"Yes, I absolutely would," Cain answered. (Video below). He added that he has already discussed the possibility with his attorney.

The Republican presidential hopeful said he doesn't know Sharon Bialek, the woman represented by attorney Gloria Allred, nor does he even remember her name. He said he watched their press conference Monday from a hotel room.

"I don't even know who this woman is," he told reporters Tuesday. "I tried to remember if I remembered that name, and I didn't."

Bialek on Monday became the first woman to give details of alleged sexual harassment at the hands of Cain. Prior to that, Politico and other outlets reported that the National Restaurant Association, which Cain ran in the 1990s, settled some claims of harassment involving Cain but no details, including names of the accusers, were attached to those stories.

"I repeat. I never acted inappropriately with anyone. Period," Cain said. "And these accusations that were revealed yesterday simply did not happen."

Cain said during his televised press conference Tuesday that, with Bialek, the "Democrat machine in America has brought forth a troubled woman" to accuse him of sexual harassment in an attempt to harm his candidacy.

"The machine to keep a businessman out of the White House is going to be relentless," he said.

Reports have since surfaced that Bialek has had legal and financial troubles in the past, and a reporter on Tuesday asked Cain whether her history was relevant.

"From a common-sense standpoint, one would have to ask if in fact that might not have been a motivation for her being subjected to this," he said.

Cain also pleaded with the media "not drag my family into this," and accused some journalists of "stalking" a few of his family members.

"I ask you as professionals to direct your questions, your ciriticisms, toward me, not my family," he told the reporters on Tuesday.

And he said he will not bow out of the presidential contest.

He ended by declaring that he wouldn't shy from questions about the accusations that have hounded him the past few weeks, and the journalists in attendance applauded.