Mitt Romney’s presidential campaign is obsessed with the women’s vote.

On the day after Rick Santorum dropped out of the race and removed all doubt Romney would be the nominee, the campaign issued five press releases within three hours on the theme that President Barack Obama’s economic record has failed American women: one featuring comments by Romney, four highlighting remarks by female Republican politicians supporting him.

It might be a good strategy, if the women’s vote existed.

Romney and the Republican National Committee argue that Obama’s energy policy is making women pay higher gas prices; that his economic policy is disproportionately costing them jobs; that the Obama White House pays female aides less than male ones. The RNC has been especially eager to repeat former aide Anita Dunn’s claim (which she later said was taken out of context) that although Obama himself was blameless, his White House was “a genuinely hostile workplace to women.”

Everyone understands why Republicans are mounting this attack. They are responding to weeks of Democratic charges that they are waging a “war on women.” A recent USA Today/Gallup poll that found Romney losing support among women younger than 50 in swing states has especially alarmed them.

But what’s mystifying is just which women Republicans are trying to reach. The number of voters who are deeply concerned about the treatment of Democratic women in the White House and will vote for a Republican as a result has to be, as a rough approximation, zero. Ditto for the number of voters who are especially concerned about high gas prices not because they themselves are paying them or because everyone is but because women, as a group, are. I suspect that not many people think that way, and those who do lean pretty strongly Democratic.

The evidence that Romney is lagging in the polls because voters are upset about a “war on women” — rather than because of a bruisingly negative primary campaign or the recovering economy — is pretty thin. But Republicans are responding not just to the polls but to the persistent mythology of the gender gap.

Ruth Marcus of the Washington Post recently fell prey to this conventional wisdom, writing that “the GOP has suffered from a gender gap in every presidential election since 1980.” Suffered? Of the eight presidential elections from 1980 to 2008, Republicans won five (four if you exclude 2000). Republicans carried women, albeit narrowly, three times; Democrats carried men twice. Republican can lose even while winning men, as in 1996. Democrats can lose while winning women, as in 2004.

The evidence suggests that women are more inclined than men to vote for Democrats, but this gap doesn’t consistently help either party. It isn’t the case that the larger the gender gap, the worse Republicans do. Republicans did seven points better among men than women in 2004, when they won. They did five points better in 2008, when they lost.

Obama barely won men in 2008. If this race is at all competitive, he will lose them this time. And that’s not all we can predict. Romney will win among large subgroups of women: those who are married, those who are white, those who go to church regularly. Gender isn’t the principal determinant of women’s votes any more than it is of men’s.

And making an issue of the statistics about job loss by gender will come back to haunt Republicans. Romney claims that 92 percent of those lost since Obama took office belonged to women. Does he have any plan, as president, to ensure that women get the right percentage of jobs? Does he realize that cuts in aid to state governments — like the Medicaid cuts that are an important part of his agenda — would inflict disproportionate job losses on women?

Of course, Romney should use female campaign surrogates. (He should especially continue to highlight his wife, Ann, who is likely to wow both men and women.) When he is talking about how his economic policies will create jobs, he should highlight women — as well as men — who own small businesses.

But his overall support among men and women alike is what needs boosting. It’s a mistake for Romney to think he has a special problem with women, or that he can solve it by making a gender-specific appeal.

Republicans deserve credit for resisting the idea — the lazy instinct, really — that what female voters care most about are stereotypically “women’s issues.” The party should take the further crucial step of seeing that women don’t have to be courted on the basis of their sex at all.

Ramesh Ponnuru is a Bloomberg View columnist and a senior editor at National Review.