A Pew poll out earlier this week that caused Democrats nine kinds of heartburn included the startling suggestion that women were hopping off the Obama train faster than you could say “woman’s right to choose.”

(Carolyn Kaster/AP)

As Andrew Sullivan put it in his piece headlined ‘Did Obama Just Throw the Entire Election Away?‘ the post-debate 12-point swing recorded in that survey was a doozy, and then there was this: “That [18-point] gender gap that was Obama’s firewall? Over in one night.” 

Well, not quite. Though that one poll showed the race dead even among female voters, 47 to 47, even Sullivan’s hair is no longer on fire, and some subsequent polling has been a lot less devastating for Obama. A CNN poll of likely voters in Ohio shows Obama leading Romney among women 60 to 38, and a New York Times poll has Obama ahead with women 51 to 45 in Colorado, 56 to 40 in Virginia and 53 to 43 in Wisconsin.

Still, yes, there has been some weakening of Obama’s favor among women, as we often react to events in much the same way as, you know, other humans. “I believe there has been erosion post-debate,” said the Democratic pollster Anna Greenberg, “so there has to be erosion among women, too.” 

Mitt and Ann Romney (Evan Vucci/AP)

As we’re 52 percent of the population, we not only aren’t but could never be a monolith; Greenberg jokes that in her view, it would make more sense to have a ‘Men for Obama,’ campaign than ‘Women for Obama’ outreach, since the male cohort is “a smaller, more homogenous group.”

So, were all those abortion-rights shout-outs at the Democratic National Convention just a month ago for naught, and the whole last year of talking about women an utter waste? No, but Greenberg says what drew women to Obama in the first place was always broader than that: “It wasn’t just the discussion of choice,” she said, so much as a combo of “ick” factors including Missouri senate candidate Todd “legitimate rape” Akin, the naked pandering of Ann Romney’s  strange “I love you, women,” call from the Republican National Convention stage in Tampa, Republicans in Virginia, Texas and elsewhere in the land chasing pregnant women around with transvaginal probes, and Romney’s refusal to even say whether he’d support the Lilly Ledbetter Act assuring women equal pay. All that and more — talking to you, Rush — “activated every Democratic impulse” among women, who historically have favored the blue team anyway.

Still, women saw the same first presidential debate men did last week, and some decided to give Romney a chance as a result — largely, in Greenberg’s view, because the president failed to convey that he understands what Americans struggling in this economy are going through.

Hopefully, he’ll do more of that in his next outing. But from what I can tell, the Obama team’s effort to make sure women aren’t abandoning the president en masse seems mostly to be focused on still more talk about choice.

The president and his surrogates gleefully pounced on Mitt Romney’s supposed attempt to fool women into thinking he supports abortion rights, though that’s not what I heard him say. And the first lady looked like she was going to cry when she talked on the stump this week about how reliably, solidly and down-to-the-bone pro-choice her husband is.

But since women are as closely divided as the population as a whole is on the abortion issue — with 49 to 45 percent favoring abortion rights, according to a recent USA Today-Gallup survey — the appeal to us has got to be significantly bigger than that.

In fact, the moderate, late-deciding, majority-female swing voters who the campaign still needs to reach at this point are not really the best audience for the one-note message that even the most casual news consumer must have fully grasped by now.

My Post colleague Karen Tumulty, who has written about Obama’s advantage with women in the key swing state of Virginia, notes that there has been a huge racial disparity in polling there, with Romney actually winning by 8 points among white women but Obama winning non-white women 91 to 8. Surveys there have also found that men and women held nearly opposite views of which candidate was better on the economy: Women said Obama was superior on that front, 52 to 39, while men said it was Romney, 51 to 40.

It’s on that issue that Obama has to make his case with both men and women if he really intends to win this thing. And maybe if there were more women in his inner circle, he’d know that.

Melinda Henneberger is a Post political writer and anchors the paper’s ‘She the People’ blog. Follow her on Twitter at @MelindaDC.