In an e-mail to supporters Monday evening, Cain denounced the media as "obsessed with nonsense" and of "trivializing" his experience.

If there is any consolation for Cain, it is that a plurality of Republican voters did not believe the claims to be true. Of Republicans, 39 percent said they thought the claims were false, while 29 percent said they were true. A third of Republican voters said they weren't sure.

Republican women were especially unconvinced - 46 percent believed the allegations to be untrue, versus only a third of Republican men.

Democrats were less forgiving, with a majority - 51 percent - believing the allegations had merit. Male and female Democrats were both largely more likely to believe the accusations.

But there is evidence that the allegations are permeating the national consciousness. Three-quarters of those surveyed - and 77 percent of Republicans - said they had heard of the allegations. This was before the Bialek allegations, which look to reinvigorate the media scrutiny into Cain's behavior.