Cain's wife Gloria, who has maintained a low profile so far on his campaign, gave a televised interview in his defense.
"You hear the graphic allegations and we know that would have been something that’s totally disrespectful of her as a woman," Cain told Fox News earlier this month. "I know the type of person he is. He totally respects women."
Cain has denied all allegations and maintained on Tuesday that he has no plans to drop out of the race.
"The definition of reassess is: To consider again, esp. while paying attention to new factors. Doesn't sound like dropping out," Cain's team tweeted prior to the speech.