'Did not happen'

Republican presidential candidate Herman Cain Tuesday emphatically denied accusations of sexual harassment, insisting he did not remember the face, name, or voice of one of his accusers who went public on Monday. Cain said he watched her on television in his hotel room and went over and over in his mind for some memory of her but could not recall knowing her.

"The charges and the accusations I absolutely reject. They simply didn't happen," Cain repeated at a news conference. "They simply did not happen."

Cain stood at a podium in front of cluster of American flags and bluntly struck back at Sharon Bialek, who is publicly accusing him with the assistance of activist attorney Gloria Allred. Bialek, 50, is a former Chicago-based employee of the National Restaurant Association who said Cain, then CEO of the association, reached under her skirt 14 years ago when she approached him for help finding a new job.

Calling Bialek a "troubled woman," Cain took questions and directly addressed the nine-day media firestorm for nearly 30 minutes in a press conference. "I have never acted inappropriately with anyone. Period," he said twice.

Four women have made sexual harassment accusations against Cain, two anonymously. One of his original two accusers was interviewed by The New York Times and was identified publicly as Karen Kraushaar, who is now a spokeswoman in the Treasury Department's office of inspector general for tax administration.

When asked about Kraushaar, Cain said he recalled her accusation of sexual harassment but insisted that "it was found to be baseless."

Cain, who has polled strongly in the GOP presidential race since surging to a Sept. 24 Florida straw poll win, said he would not quit: "As far as these accusations causing me to back off and maybe withdraw from this primary race, ain't gonna happen, because I'm doing this for the American people, and the children and grandchildren."

Calling the accusations an effort to distract voters and part of the problem with a "broken Washington," Cain cast blame on the Democratic machine. Although he promised the tough going would not drive him from the race, Cain warned supporters there might be more accusations: "The machine to keep a businessman out of the White House is going to be relentless."

Cain said his wife of 43 years responded with disbelief to Bialek's story. He then urged the media to leave his family alone and address questions only to him: "I will vigorously defend my reputation."

Cain, who said he would consider a lie detector test, has received an outpouring of support from his backers and is confident most of his supporters will not believe the accusers. But he acknowledged that other voters would naturally be repelled by the accusations.

Other GOP presidential hopefuls have been asked to respond to the accusations, but have avoided going on the attack. Mitt Romney has called the accusations "disturbing." Asked about Romney's remark, Cain agreed with the characterization but stated again that the accusations are false.

Cain said he only remembers one complaint of sexual harassment, a matter that was found "baseless." The woman reportedly was paid an undisclosed sum in her departure by the National Restaurant Association, an action that Cain refuses to call a settlement because there were no legal implications. Instead, it was a separation agreement handled as a personnel matter, he said.

In that case, he reiterated that his only recollection is an incident in which he gestured-placing his hand beneath his chin-and said that the woman was the same height as his wife, Gloria. That was the only incident he described, noting that they were not alone at the time, and that he generally saw that employee at planning meetings.

"I can't tell what their motivation is," Cain said of his accusers, "other than to stop Herman Cain."

The Associated Press contributed to this report.