Defiant Herman Cain said he would not drop his bid for the Republican presidential nomination

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.

"Ain't gonna' happen," Cain said at a news conference 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 behavior 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."