Three prominent female Democrats all but openly began running for president this week, taking their most active steps yet to challenge President Donald Trump and claim leadership of a movement of moderate and liberal women that has come to define their party during the 2018 elections.

Sen. Kamala Harris of California on Friday took the stage in a church in the early primary state of South Carolina, as an audience chanted: “Madam president!” A day earlier, Sen. Kirsten Gillibrand of New York visited similarly crucial New Hampshire, calling the November election a pivotal moment for women. And Sen. Elizabeth Warren of Massachusetts left little doubt about her intentions when she released a genetic test indicating she has American Indian ancestry — a move to blunt Trump’s taunts alleging she had mischaracterized her heritage.

These women are beginning to offer themselves as potential presidents at a time when stark divides around gender are shaping the midterm campaigns: A record number of women are running for Congress, mainly on the Democratic side, and polls show women favoring Democrats by a huge margin. Yet Trump has begun sharply assailing the #MeToo movement and making increasingly explicit appeals to male identity.

Gillibrand, who touted a paid family leave proposal beside Molly Kelly, New Hampshire Democrats’ nominee for governor, in a Concord candy shop Thursday, predicted multiple women would run against Trump in 2020. She said she had made no decisions about her future, but cast the political moment as one of women mobilizing against a “credibly accused sexual harasser and sexual assaulter” — Trump.

Gillibrand, 51, said the political energy among Democratic women this year far exceeded anything she saw in 2016, when Hillary Clinton stood a chance of becoming the first female president. Alluding to the Women’s March of 2017 and the recent protests against Justice Brett Kavanaugh’s nomination, she said that energy would help define the 2020 election.

“It will carry over to the presidential race,” Gillibrand said in an interview. “You’ll have many women running. It’s not going to be just one woman running.”

It would be unprecedented for multiple women in high office to seek a party’s presidential nomination in the same year, and it could create an unpredictable dynamic in the primary — potentially dividing voters determined to nominate a woman and perhaps heightening scrutiny of how male candidates have treated women in public and private life.

Harris and Warren have both confirmed they are considering the 2020 race, while Gillibrand has been exploring a campaign without saying so definitively. A fourth senator, Amy Klobuchar of Minnesota, has drawn wide interest as a potential candidate without taking active steps to prepare.

If multiple women run, no one Democrat could monopolize the vision of breaking a glass ceiling, as Clinton did in 2016. And any Democratic woman might face anxiety, expressed quietly by some concerned party members, about the ferocity with which Trump has savaged his female critics.

But some Democrats say electing a woman is even more important now than in 2016. And many Democratic leaders believe the political mood in the party could quickly catapult one or more women to front-runner status.

Mayor London Breed of San Francisco, the largest U.S. city with an elected female mayor, said Democrats had been rallying to female candidates in the midterms and there was an opportunity — “now more than ever” — for a woman to lead the party. Breed said she would back Harris if she runs.

“We’re overdue, let’s put it that way,” Breed said in an interview. “It would be great to finally see a woman step up and run this country.”

Trump, who has issued blanket denials of numerous allegations of sexual misconduct, maintains strong support among conservative women and carried a majority of white women against Clinton in 2016. But his current standing with female voters is dismal: Women disapprove of his job performance by a 2-1 margin, while men are evenly split, according to the Pew Research Center.

Trump now regularly criticizes #MeToo, and at a recent rally he mocked Christine Blasey Ford, the woman who said Kavanaugh assaulted her. The president often singles out female Democrats for ridicule, including Warren, Rep. Maxine Waters of California and Rep. Nancy Pelosi, the House minority leader.

Harris, 53, told reporters in a Greenville library Friday morning that matters of economic policy and identity had to be intertwined in the Democratic agenda. Having clashed with Kavanaugh in the Senate, Harris said the country was perched at an “inflection moment,” including on matters of gender and sexual assault.

“These are not mutually exclusive issues, to talk about race and gender equality and all of those things, and to talk about economic well-being,” said Harris, who is due to visit the leadoff caucus state of Iowa next week.

And last month Warren, 69, borrowed the language of #MeToo, declaring it was time to elect a female president and tell Washington: “Time’s up.”

That message resonates with voters like Jewels Morgan, a biologist who held a figurine of Warren as the real-life version campaigned last week at Clayton State University in Georgia. Warren, best known as a critic of corporate power, classed women with blacks and students as groups oppressed by a “rigged system.”

Morgan, 41, said it was “extremely important” to elect a woman president, naming Warren as a favorite alongside Harris and Sen. Mazie Hirono of Hawaii, also a critic of Kavanaugh.

“Trump being elected in 2016 really opened up a lot of avenues for women to finally stand up for ourselves and show that we are every bit as amazing as guys are,” Morgan said, “and that we have the ability to run this country.”

The results of November’s elections could supercharge that mood, if they yield strong gains by Democratic women.

But if Republicans keep power in Congress and the long-anticipated “Year of the Woman” fails to materialize, it could demoralize Democrats and stoke suspicions, already simmering in some precincts, that a white man would stand the best chance of unseating Trump.

Kathleen Sebelius, the former Kansas governor and federal health secretary, said Democratic primaries had channeled a clear signal from liberal-leaning women. But she said the more decisive test would come on Nov. 6. Sebelius said there was plainly a demand for candidates who “push back against the misogyny and the hate speech and the rhetoric that often is permeating D.C.,” and the midterms would expose how powerful that demand is.

“What we don’t know, really, until November, is whether that is a broad constituency that spans parties and includes independent women and Republican women, and men,” Sebelius said, adding: “A lot of us still have PTSD from 2016.”

The Democratic primary field is likely to be crowded and diverse, and there is no sign that Democratic men intend to mute their ambitions in 2020. But a primary defined by gender could imperil some men: Joe Biden, the former vice president, has been struggling to address his role leading the 1991 Clarence Thomas-Anita Hill hearings. Michael Bloomberg, the former New York City mayor, recently drew backlash for questioning elements of the #MeToo movement.

Tom Steyer, a billionaire Democratic activist who has entertained his own challenge to Trump, said he did not believe a candidate would have to be female to campaign as a champion of women.

“I go to a lot of Democratic events, and I know how much of the work and time is done by women,” Steyer said, arguing that identity alone should not be a decisive credential: “Does that mean that you have be gay to think that prejudice and discrimination against gay people is wrong? I don’t think so.”

Gillibrand warned in Michigan that there was still deep discomfort with progressive gender values in powerful institutions, adding that the Democratic Party “is not immune.” But she said the party’s 2020 standard-bearer must be deeply invested in the fight for women’s equality.

“No one in the Democratic Party should be outside this moment,” she said. “Because if they are, they’re out of touch.”