SCOTTSDALE, Ariz. (AP) - A defiant Herman Cain declared Tuesday he would not drop his bid for the Republican presidential nomination in the face of allegations of inappropriate sexual behavior.
"The charges and the accusations, I absolutely reject," he said at the news conference. "They simply didn't happen. They simply did not happen."
Would he end his Presidential campaign over the accusations? "Ain't gonna happen," he said a day after a fourth woman accused him of unwanted sexual advances.
"We will get through this," he added, trying to steady a campaign that has been rocked by the controversy for the past 10 days.
Cain denied anew that he had ever behaved inappropriately and said the alleged incidents "they simply didn't happen." He said he would be willing to take a lie detector test if he had a good reason.
Earlier in the day, Cain sought to undercut the credibility of the latest woman whose accusations are threatening his Republican presidential campaign. His chief rival, Mitt Romney, weighed in for the first time, calling the allegations "particularly disturbing."
Cain said he called the news conference because he wanted to speak directly to the public, accusing the media of distorting his response to the allegations. He said that had never seen Sharon Bialek until she called her news conference on Monday in New York, alongside attorney Gloria Allred.
"I don't even know who this woman is," he said of Bialek. "I tried to remember if I recognized her and I didn't."
Another name confronted Cain, as well, when one of his two original accusers gave an interview to The New York Times and was identified publicly by news organizations including The Associated Press as Karen Kraushaar, 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 "it was found to be baseless."
Cain contended that "the Democratic machine" was pushing the allegations but said he could not point to anyone in particular. He also suggested his accusers were lying.
Earlier, Romney, the former Massachusetts governor who has been a GOP front-runner for months, told ABC News/Yahoo! the allegations were serious "and they're going to have to be addressed seriously." He called the latest accusations disturbing, and Cain didn't disagree, both in an earlier interview and at the news conference.
"He's right. They are disturbing to me," Cain said. "They are serious. And I have taken them seriously."
But they're untrue, he declared.
"I reject all of those charges," he said, adding that "I have never acted inappropriately with anyone" and didn't even recognize Bialek.
Cain said it was "a remote possibility" when asked if it were possible he would recall Bialek's alleged incident in the future. "I seriously doubt I'm going to have an `a-ha' moment later," Cain said.
Prominent Republicans pressed for a full accounting.
"Get all the facts in front of people, otherwise he's going to have this continuing distraction," Mississippi Gov. Haley Barbour, a former Republican National Committee chairman with deep ties to the GOP establishment, told MSNBC.
Though recent polling shows Cain still doing well, party operatives suggested it was only a matter of time before his political standing could suffer.
"Herman's base is going to stick with him," said Republican strategist Rick Tyler, Newt Gingrich's former spokesman. "But the average Republican voter who is not as engaged as intensely in the race, is sick of this and, for Cain, the concern is they will pass on it and pass on him."
Cain looked to keep those supporters in his corner.
"We are not going to allow Washington or politics to deny me the opportunity to represent this great nation," he said. "As far as these accusations causing me to back off and maybe withdraw from this presidential primary race? Ain't gonna happen. Because I'm doing this for the American people, and the children and the grandchildren."
There were growing signs of unease in conservative circles as the Georgia businessman tried to stem the controversy in its second week.
"If there is a pattern then it's a part of his character and then, yes, it is going to matter," Tony Perkins, head of the conservative Family Research Center, said in an interview.
An upstart in the presidential race, Cain shot to the top of opinion polls and emerged in recent weeks as Romney's main conservative opponent, with tea party activists and other conservatives flocking to the former pizza company executive's tell-it-like-it-is style and outsider image.
But he's spent the past 10 days battling accusations from women that he acted inappropriately toward them while he headed of the National Restaurant Association in the 1990s.
Cain's campaign issued a tough statement by Tuesday about Bialek, the most recent accuser, including references to civil lawsuits in the Cook County Court system in Illinois allegedly relating to her and cited news reports of her involvement in a paternity case and a bankruptcy filing.
"In stark contrast to Mr. Cain's four decades spent climbing the corporate ladder rising to the level of CEO at multiple successful business enterprises, Ms. Bialek has taken a far different path," the campaign said.
It also questioned whether Bialek had a financial interest in stepping forward.
"Who is financing her legal team, have any media agreed to pay for her story, and has she been offered employment for taking these actions?"
In a round of media interviews early Wednesday, Bialek was asked repeatedly about her motives in speaking out after staying quiet for 14 years.
"I'm just doing this because it's the right thing to do," she said. She said she was neither paid nor offered a job to go public with her allegations. She said she waited so long to come forward= because "I was embarrassed ... and I just kind of wanted it to go away."
She said she wasn't paying a fee to Gloria Allred, the attorney whose name has become synonymous with women's rights issues.
At least two women who worked at the restaurant association the same time as Cain filed sexual harassment complaints with the trade group and received financial settlements.