Those numbers may validate popular narratives that Cain is slipping amid allegations of sexual harassment during his time as president of the National Restaurant Association, while Romney is unable to attract Republicans beyond his core constituency. Gingrich, the conventional wisdom goes, could be where conservative Republicans defect if Cain proves untenable.

But there were some encouraging signs for Cain. Seventeen percent of women chose Cain despite the allegations, more than any candidate other than Romney. And Cain's support seems concentrated among older Republicans, who traditionally are among the most likely to vote.