11/11/2011 10:23 am ET Updated Jan 11, 2012

Herman Cain Losing Support Of Women Voters After Sexual Harassment Allegations, Poll Shows

WASHINGTON -- CBS News has a new poll up on the GOP presidential race. And while the top line numbers seem relatively unchanged -- Newt Gingrich is rising, Mitt Romney remains near the top, Herman Cain is leading -- the takeaway narrative isn't all that good for the former Godfather's Pizza CEO.

"Cain has lost support among women since last month -- from 28 percent in October to 15 percent now," the poll reveals.

The problem, naturally, is the series of past sexual harassment allegations that have been leveled at Cain in recent weeks. At least four women have claimed Cain harassed them while he headed the National Restaurant Association in the late 1990's, claims that have likely persuaded 30 percent of all respondents to say that they are now less likely to back his candidacy. That number rises to 38 percent when restricted to female respondents.

And yet, Cain has some staying power. Though it is a national poll, which carries less weight than a poll of Iowa or New Hampshire voters, Cain still leads with 18 percent, followed by Romney and Gingrich, who are both at 15 percent.

"Support for both Cain and Romney has declined since late last month, and Gingrich is the only one of the top three whose support is steadily -- if slowly -- on the upswing."

One caveat: Seventy percent of respondents said it is still too early to pick a candidate.

UPDATE: Making matters worse for Cain: He wasn't doing too well with women voters in the first place. As the Center for Responsive Politics reported, even before the sexual harassment allegations surfaced, the Cain campaign was struggling to secure money from women donors.

In terms of receiving political donations from the ladies, Cain's fund-raising so far this year has been slightly lower than nearly all of his rivals.

For its part, Cain's campaign has relied on women for about 25.1 percent of its money, according to estimates by the Center for Responsive Politics. That ranks Cain behind all but two other current candidates.