This week, as Senate Republicans killed a bill that would have helped close the gender-based wage gap, the Grand Old Party continued to twist itself in rhetorical knots. They simultaneously argue that they understand the bread-and-butter economic issues that worry women most, and that women—who know they make less money than men for the same work—don’t make less money than men for the same work.

Never mind that study after study confirms that even when you control for variables like profession, education, hours worked, age, marital status, and children, men still are compensated substantially more—even in professions, like nursing, dominated by women.

No wonder there’s a gender gap.

Republicans, it seems, are finally taking steps to try to narrow it. On Monday, the Romney campaign named Rep. Cathy McMorris Rodgers, an up-and-coming Republican from Washington state, as its liaison to the House. But even as her appointment put a woman in a visible and influential role at a time when the campaign desperately needs both the symbolism and the substance of such a high-level female advisor, McMorris Rodgers was denying that it had anything to do with gender. “I don’t think this is related to women or the women’s vote,” she told Politico.

No one could credibly claim that McMorris Rodgers’ gender was the only reason she was chosen. As vice chair of the Republican Conference, she’s already a member of the party leadership (and its highest ranking woman). She’s a conservative from a blue state. And she endorsed Romney beforehe had a lock on the nomination. So there were lots of reasons she was chosen. Why not embrace the idea that gender was one of them?

Clearly, women are under-represented at all levels of government and politics. While women make up slightly more than half the country’s population, they account for only 17 percent of Congress—and less than 10 percent of the Republican House caucus (24 out of 242). Increasing their numbers and visibility—on both sides of the aisle—seems like a worthy goal. That is, if you believe that women bring a different and valuable perspective to their various roles.

At one level, that seems to be exactly what a lot of Republican women are saying.

A few weeks ago, the 24 female Republican House members launched the Women’s Policy Committee to help their party communicate more effectively with women. Among other things, the new group seeks to make sure women are heard on a range of issues.

“What we would like to do is make certain that men are taking into consideration what the mom in the minivan is thinking,” said Rep. Marsha Blackburn of Tennessee.

“Women need to be not tokens but legitimately at the table discussing issues with members of the House,” added Rep. Ann Marie Buerkle of New York.

But even as the Republican women are demanding a louder voice in their party’s policy debates, they’re claiming that women don’t have a problem with their policies. Equal pay? Already there. Domestic violence? Fixed that. Choice? Don’t need to go there. Not a problem if women’s bosses get to decide which procedures and medications their health policies will cover. All that “war on women” stuff, they claim, is just so much election-year posturing. Funny, but that’s not what you hear from women voters.

The sense the one party (the Democrats) is willing to address problems that disproportionately affect women, while the other (the Republicans) denies they even exist, has fueled the gender gap for decades. And it will be a factor in 2012. In 2008, women voted overwhelmingly for Barack Obama. He carried female voters by 13 points, while losing men by a whisker. And he won unmarried women by a breathtaking 41 points, while losing married women—an erstwhile reliably Republican cohort—by only a point. Moreover, 10 million more women than men voted that year, amplifying the impact of their votes.

This year, the race is certain to be closer, though President Obama continues to have a healthy lead among female voters in most polls. But as long as the G.O.P., led by its increasingly visible women, continues to insist that the problem is not their policies but women’s failure to understand their own lives and interests, the gender gap won’t go away.