Mitt Romney’s electoral trouble with women — more precisely with college-educated women — is real enough. Recent polling has Romney trailing President Obama by 18 points among this group in Ohio, with similar gaps in other battleground states.

The media — ever drawn to simple explanations that reinforce their own cultural expectations — have diagnosed Romney’s gender-based electoral weakness as the result of his opposition to the contraceptive mandate. This is both initially plausible and demonstrably false. More than 60 percent of American voters don’t even know Romney’s position on the mandate — a topic they rank near the bottom of their political concerns. And when pressed, a majority of women affirm that religious institutions should be exempted from the mandate.

This is not particularly good news for Romney. His difficulties would not be solved by handing out the pill at his rallies or by a balloon drop of inflated condoms at the Republican convention in Tampa. The GOP’s main problem is not the contraceptive issue; it is the perception that it has become too ideological on many issues. Women and independent voters have seen a party enthusiastically confirming its most damaging stereotypes. The composite Republican candidate — reflecting the party’s ideological mean — has been harsh on immigration, confrontational on social issues, simplistic in condemning government and silent on the struggles of the poor. How many women would find this profile appealing on eHarmony?

This is the hidden curse of the Republican congressional triumph of 2010. Republican activists came to believe that purity is all that is necessary for victory. But a presidential candidate, it turns out, requires a broader ideological attraction than your average tea party House freshman.

Republicans forget how they have recently won the presidency. In 2000, George W. Bush campaigned — in both the primaries and the general election — on increasing the quality of education for poor children, on humane immigration reform and on expanding care by faith-based organizations for the addicted and homeless. These issues were personally important to Bush. They also signaled to independents and women that he could think beyond normal ideological boundaries. This form of “compassionate conservatism” is now broadly reviled among conservatives. The need for an analogous agenda, whatever it is called, remains unchanged. To secure a decent shot at this election, Romney will need to offer some positive vision for the common good.

This is not hopeless. A number of eventual presidents, including Ronald Reagan and Bill Clinton, emerged weakened from their nomination battles. And Romney is not a radical figure. During the heat of the primaries, he was accused of being a closet pragmatist. Now he can finally come out.

Romney’s frequent challenge is the clumsy literalism of his messaging. Faced with broad suspicion among Latino voters, Romney recently explained in Middleton, Wis.: “We’re going to have to make sure that, as we speak to Hispanic voters, that we say, ‘We’re not anti-immigrant.’ ” A better approach would be actually to speak to Hispanic voters instead of commenting, as an observer, on his own strategy. At the same Middleton event, Romney said, “We have work to do to make sure we take our message to the women of America.” Taking that message to women does not consist of repeatedly mentioning the word “women.” And it certainly does not require the transformation of religious institutions into administrative divisions of the state in the name of women’s rights.

Mainly, women and independents want some reassurance that Republicans give a damn about someone other than Republican primary voters. It is not a high bar. But Romney needs to start somewhere — to pick an issue of justice and equity that he cares about deeply. It could be lowering an unemployment rate that is now more than 40 percent among African American teenagers. Or the improvement of high school dropout factories attended by 38 percent of black students and 33 percent of Latino students in America. There are plenty of sound conservative and free-market reforms that can be applied to improving the lives of the vulnerable.

A successful presidential candidate must have a compelling economic message. But he must also be able to stand before the nation and say: “I will serve all American citizens, whether they support me or not. My conscience, my faith, my view of America requires it. It hurts us all when any are hopeless.”

One of the best ways to appeal to women — and to humans, for that matter — is to show some humanity.