The poll also indicates that 14 percent back Cain, down 11 points from last month. Four women have alleged that Cain sexually harassed them during the late 1990s when he headed the National Restaurant Association. Cain denies the allegations.

“Cain is struggling with the charges of sexual harassment, and while most Republicans tend to dismiss those charges, roughly four in 10 Republicans think this is a serious matter and tend to believe the women who made those charges,” CNN Polling Director Keating Holland said.

The survey indicates that only a bare majority of Republicans tend to believe Cain, and more than a third say he should end his presidential campaign. Among the general public, Cain has a bigger credibility problem – 50% of all Americans say they tend to believe the women and only a third say they believe Cain.