Republican presidential candidate Sen. Ted Cruz (R-Texas) speaks at the National Federation of Republican Women convention in Phoenix on Saturday. (Cheryl Evans/AP)

Sen. Ted Cruz strode through a resort here, past booths selling elephant-print scarves, “gently loved furs” and rhinestone pins spelling out presidential candidates’ names — and headed straight into a crowd of screaming women.

“Oh, my God,” one exclaimed as she spotted Cruz walking toward her at the National Federation of Republican Women’s annual conference.

Cruz (R-Tex.) came here Saturday on a mission to court female Republican activists. His timing may be opportune: As front-runner Donald Trump has come under fire for a string of comments many see as anti-women, Cruz is trying to seize the moment to retain and expand his foothold in the GOP electorate.

He also is trying to disprove the axiom that a candidate with a largely evangelical and socially conservative base can’t win over female voters.

“I’ve got to tell you, the women in here, this is a room of patriots,” he told the crowd in Phoenix. “This is a room of fighters. This is a room of women that stand up and win elections and are going to save this country.”

Cruz wasn’t the only presidential contender who saw the importance of the conference. But he was the only man. Former Hewlett-Packard chief executive Carly Fiorina addressed the group Friday night. Former Arkansas governor Mike Huckabee sent his wife, Janet. Other candidates dispatched staffers.

With the latest polls placing him fourth, after Trump, retired neurosurgeon Ben Carson and former Florida governor Jeb Bush, Cruz sees women as a key voting bloc, particularly as the huge Republican field continues to be winnowed.

“There is no force in all of politics like Republican women,” he said.

Less clear is whether Cruz, an avowed social conservative who opposes abortion in all cases, can appeal to women who are not Republican. Already, Cruz is invoked regularly to illustrate what Democrats call Republicans’ “war on women.” Those attacks would only grow should he win the GOP nomination.

On the campaign trail, Cruz has emphasized the role that powerful women have played in shaping him, including his wife, Heidi, who is on leave from her job as a managing director at Goldman Sachs, and his two young daughters, particularly the one he calls a “rascal.”

He often speaks of his mother, Eleanor Darragh, who went to college despite her father’s objections, earning a degree in math and becoming a computer programmer at Shell. She purposely never learned how to type, Cruz said, because she didn’t “want to be walking down the hall and have a man walk up to me and say, ‘Sweetheart, will you type this for me?’ ”

Heidi Cruz may be her husband’s most powerful emissary with women, in public and behind the scenes, where she courts grass-roots activists at women’s lunches, spends hours each day on the phone with donors and speaks of her faith with evangelical Christians.

She spent hours pressing the flesh at the Phoenix conference, making small talk and trying to sell women on her husband’s candidacy. She has started to make her own mark on the campaign trail, becoming a public surrogate for her husband. Over the past month, she has headlined events in South Carolina and in Texas. On Monday, she will host a meet-and-greet in Las Vegas.

In an interview, Heidi Cruz said she can articulate that her husband treats everyone equally and that, in his family, “women kind of run the show.” Issues of importance to women, she added, have expanded beyond social issues to the broad spectrum of policy.

Liberal critics have long accused Cruz of holding positions that are out of step with majority thinking on issues that affect women. Cruz has supported personhood amendments and is leading the charge to defund Planned Parenthood in the aftermath of an undercover video sting that attempted to show, but did not prove, that the women’s health organization has engaged in a black market of fetal body part sales.

“Ted Cruz is pushing the Republican Party into territory that’s further and further away from what the majority of American voters believe,” Planned Parenthood Executive Vice President Dawn Laguens said in a statement last month, when Cruz was taking a lead role in a nationwide campaign to end taxpayer support for the organization.

[Read: Cruz’s evangelical outreach shifts into high gear]

Because it has raised the specter of a government shutdown, Cruz’s charge to defund Planned Parenthood also has the potential to harm his fortunes with Republican women. In a Quinnipiac University poll of likely Republican caucus-goers in Iowa, 72 percent of women surveyed said they have an unfavorable view of Planned Parenthood; the same percentage said they support cutting off its government funding.

But 48 percent oppose shutting down the government over the issue.

[Read: GOP tries to avert shutdown as right spoils for Planned Parenthood fight]

In Alabama last month, a woman asked Cruz how he would fund women’s health services if he repeals the Affordable Care Act and defunds Planned Parenthood. He didn’t answer the question, stating only that he “feels passionately about women’s health.” He urged people to watch the controversial Planned Parenthood videos, and he railed against President Obama’s signature health-care law.

Kristen Soltis Anderson, a Republican pollster, said Cruz “understands very clearly what his brand is and would probably love nothing more than to make people’s heads spin and reach out to people others don’t think is a natural constituency.”

Cruz is also aware that many longtime activists are women and can play a crucial role in a campaign strategy based on rustling up the grass roots. He recently named a national grass-roots chair, Kaye T. Goolsby, who helped galvanize the base during his 2012 upset Senate election in Texas.

“We’ve got tremendous support among Republican women who are often the activists on the ground, who are most passionate,” Cruz said in an interview. He told the crowd he wouldn’t be in the Senate if it were not for Republican women in Texas.

“Women are the heart and soul” — “and brains!” Goolsby yelled — “and brains of the Republican Party,” he said.

For now, polls do not show Cruz clearly appealing more to women or men, either with the general public or among potential GOP primary voters.

In a national CNN/ORC poll released Tuesday, he received support from 8 percent of men and 7 percent of women. Among the general public, a late-August Quinnipiac poll showed Cruz’s favorable rating was narrowly negative among men (35 percent approving to 39 percent disapproving) and women (20 percent to 29 percent).

In contrast, Trump is viewed far worse among women (31 percent to 58 percent) than among men (41 percent to 49 percent).

Suzanne Santis and Paula Whitsell of Chula Vista, Calif., attended the conference in Phoenix. Both said they’re big fans of Fiorina, Carson and Cruz. Santis said some of Cruz’s stances, particularly on religion, are a bit far to the right for her. But she thought his message was impressive.

Both women said they support defunding Planned Parenthood and will have a hard time deciding whom to support. They were surprised and a little offended that only two candidates showed up.

“There was a huge group of women here. This is a great place to get your message out,” Whitsell said. “Those women are going to leave here and get on a plane . . . that message is going to spread like a virus.”

Scott Clement contributed to this report.