Carly Fiorina’s stock is on the rise. After a second electrifying debate performance, conservative pundits and GOP insiders hope Fiorina’s crisp command of the issues and confident demeanor will not only help end Donald Trump’s frontrunner status in the race for the Republican nomination, but will enable the Republican Party to ditch its image as just for stodgy white men.

That’s important. Since Ronald Reagan’s election in 1980, women have been far more likely than men to vote for Democratic presidential candidates. If Carly Fiorina becomes the Republican nominee for president next year, will she appeal to women voters and help close the gender gap in U.S. elections?

Probably not.

It’s true that a newer generation of outspoken conservative women like Carly Fiorina is on the rise, and could be an important development in American politics. But they still make up a minority of women in the U.S. Only one in four American women identifies herself as Republican, according to the Public Religion Research Institute’s 2014 American Value Survey.

Moreover, on the issues that will likely dominate the next election, conservative women nationally differ significantly from the more than 75 percent of American women who identify as either Democrats (37 percent) or as independents or some other party (38 percent).

For instance, overwhelming majorities of Democratic and independent women support making access to guns more difficult, keeping (or even expanding) Obamacare, raising the federal minimum wage, and raising taxes on the wealthiest Americans. All those positions are strongly opposed by Carly Fiorina.

Most American women are simply more comfortable with having a strong government social safety net and would like to see government do more, not less, to help address income inequality. For instance, the 2014 American Values Survey finds that 79 percent of independent women and a whopping 90 percent of Democratic women completely or mostly agree that government should do more to reduce the gap between the rich and the poor, compared with just 32 percent of Republican women. Studies by political scientists who study the gender gap repeatedly show that women’s support for social welfare policies are what drive women’s greater desire to vote for Democrats than men.

If the Republican Party wants more of the women’s vote in 2016, it has to get over its aversion to what it calls “identity politics.” Many conservatives reject what they view as pandering to specific interests to win their votes; they believe their message should resonate with all Americans despite their gender, race, or class.

That’s why many conservative women praised Fiorina’s answer to the CNN debate question about what women she would place on the $20 bill:

I wouldn’t change the $10 bill or the $20 bill. I think, honestly, it’s a gesture. We ought to recognize that women are not a special interest group.

This response prompted the Independent Women’s Forum (IWF), a free market think tank geared toward conservative women, to praise Fiorina for not playing the gender card. IWF’s Charlotte Hays wrote approvingly that if Fiorina is the eventual nominee for the GOP, it will

not be because she is a woman and likes to whine about it. It would be because she made it onto the ticket as a candidate with ideas and a persona (yes, Donald) that gave GOP primary voters the confidence that she could be a good president.

Whether or not Fiorina wins the nomination, the Republican Party will be facing a Democratic nominee who will directly appeal to women voters with policies that women care more strongly about than men and will market them in a way designed to maximize women’s turnout for the Democrats. This worked when Democrats used the “Republican war on women” narrative in 2012, as support for the birth control mandate helped drive women’s vote for Obama independent of partisanship, ideology, and other factors often linked to voting behavior.

If Hillary Clinton wins her party’s nomination, for example, she has made it clear that she will pursue federal legislation that would require private businesses to provide paid family and sick leave—a position rejected by Fiorina and the current crop of Republicans running for president but one that is strongly supported by most American women. Conservative leaders and the GOP have so far been unable to counter these targeted messages to women voters, which Democrats have used effectively in past presidential elections.

In recent years, right wing women’s organizations and conservative women leaders have begun to develop a gendered narrative as to why reducing the scope and size of government is ultimately better for American women and their families. If Carly Fiorina is the nominee and if she is willing and able to make a more convincing case as to why her approach to governance is better for women, then perhaps she could close some of the gender gap in presidential elections. But the public opinion data show it would be an uphill battle.