New polls conducted in the past week offer a fresh look on the nation’s - and Republicans’ - reactions to the Herman Cain sexual harassment scandal. Let’s run them down. (Despite their freshness, none of these polls was conducted after Monday’s allegations of harassment from Sharon Bialek).

Big news: Three-quarters of Americans have heard at least a little about the sexual harassment accusations against Cain and half have heard “a lot” in a poll by the Pew Research Center released Monday.

Truth? Among those who’ve heard at least a little about the accusations, about four in 10 of all adults think the they are true in the Pew survey, while a quarter see them as false and more than a third have no opinion. The numbers are reversed among Republicans and GOP-leaning independents: Roughly four in 10 say the allegations are false while three in 10 say they are true. More than half said the accusations are not a serious matter in a Post-ABC poll released Friday, while four in 10 said they were serious.

Has the press been fair? Among those who’ve heard about the story, about four in 10 Republicans in the Pew survey say press coverage has been fair, but almost as many say the media have been too tough on Cain. Roughly half of Democrats think the press coverage has been fair.

Has opinion of him changed? Cain has a 52 percent positive rating among registered voters who would vote in the GOP primary according to an NBC/WSJ poll released Monday, the same as in October. But his “very positive” ratings dipped from 28 to 20 percent since last month and his overall negative rating tripled from 6 to 19 percent. Cain’s “positive intensity score” in Gallup polls dropped from 34 in early October to 25 in more recent polling among Republicans and GOP-leaning independents. The score is simply the difference between “strongly favorable” and “strongly unfavorable” views of a candidate, among those who have an opinion.  

Will it change your vote? Almost seven in 10 Republicans and GOP-leaning independents in the latest Post-ABC poll said the Cain situation won’t make any difference in their vote, while almost a quarter said it would make them less likely to back him. The NBC/WSJ poll finds a similar result, with 54 percent of registered GOP primary voters saying they are not at all concerned about voting for him in light of the allegations, another 15 percent saying they’re “just a little concerned.”

What does it all mean? Cain’s continued strength against Mitt Romney and other candidates (he is within one percentage point of Romney in all three new polls) shows that most of his supporters are sticking with him and skeptical of recent sexual harassment claims. Nevertheless, Republicans who were less familiar with Cain a month ago are seeing him in a more critical light, a development that could keep him from expanding his base of support and surpassing Romney.

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