Updated 11/8/11 – 9:10 p.m.

(CBS) — Republican presidential candidate Herman Cain strongly denied sexual harassment allegations brought by a Chicago woman, saying he doesn’t even remember meeting her.

Sharon Bialek on Monday said Cain groped her in a car in Washington, D.C., more than a decade ago.

“I don’t even know who this lady is,” said Cain. “I went over and over in my mind, do I know this lady? The answer was no.”

According to a report from the Chicago Sun-Times, Cain and Bialek were seen speaking at a Tea Party event last month. The report claims that the two “hugged each other backstage in a full embrace like old friends.”

Cain faced the media on Tuesday in Phoenix and was asked to explain how several women could make similar allegations of sexual harassment.

“Some people don’t want to see Herman Cain become president of the United States of America,” Cain said. “I can’t tell you want her motivation is, other than to stop Herman Cain.”

He also put to rest any questions that he would drop out of the race.

“Ain’t gonna happen,” Cain said.

Cain said he absolutely would take a lie detector test to prove he’s telling the truth, but he’s not going to do that unless he has good reason.

He also said he believes character and integrity should come under the microscope in the race for president, but with a qualifier: with facts, not accusations.

Bialek said Tuesday on the CBS Early Show that Cain should just admit to what happened.

“I don’t despise the man,” she said. “I actually did it because I want to help him. I want to give him a platform to come clean; to tell the truth, and he still hasn’t done it, and it’s really a shame.”

Bialek said someone needed to come forward with allegations.

“I wanted to be the voice and the face for those women who couldn’t or wouldn’t come forward, and those that know me know that I’m pretty outspoken and I fight for my convictions, and I really believe in this and I have to do something,” she said.

CBS 2’s Mai Martinez reports Bialek’s claims are potentially the most damaging for Cain so far, not just because she was the first accuser to come forward publicly, but because she left little to the imagination about the alleged harassment.

“He suddenly reached over and he put his hand on my leg, under my skirt and reached for my genitals,” Bialek said of her encounter with Cain in 1997. “He also grabbed my head and brought it towards his crotch.”

Bialek worked for the Educational Foundation of the National Restaurant Association in 1996 and 1997. Cain ran the trade group at the time and Bialek said she first met him at a trade convention.