When Kirsten Gillibrand tells people she’s running for president, she often talks about running as a mother.

Being a woman and a mother is central to the New York senator’s political message, a defining note even if not always intentionally so, as her campaign trail anecdotes continually drift back to it.

She says she views the world through a mother’s eyes, caring for the children of America and the world like she does her own. It is part of her origin story, of her first visit to a campaign headquarters with her grandmother, of how a past opponent dismissed her as “just a pretty face”. To many in America, it was the senator’s commitment to speaking out against sexual misconduct that drove her rise.

In a traditional election year – pretty much every one the US has had so far – being a woman with a defining, defiant and unapologetic voice would be enough to separate her from the competition, who would be men. But this election is different.

It comes after Donald Trump’s victory in 2016, a campaign in which the Republican candidate made derogatory comments about female critics and weathered accusations of sexual misconduct and even the unearthing of a tape in which he said he could “do anything” when trying to seduce women, even “grab them by the pussy”.

We have different life experiences. We might see different problems. We might see different solutions Kirsten Gillibrand

It comes after a wave of female-led protest marches against Trump, after allegations against Harvey Weinstein led to sexual misconduct allegations against powerful and famous men that snowballed into the #MeToo movement. And it comes after more women then ever entered Congress via the midterm elections.

There are six women running – so far – in the Democratic primary. Being a woman and a feminist is part of their campaigns. For candidates like Elizabeth Warren, feminism is not necessarily the defining message or what they are best known for.

“I think it’s amazing that we have at least six women running for president right now,” said Gillibrand at a campaign stop in New Hampshire’s capital, Concord, on Friday.

“Because not only does it give the American people a chance to see what leadership looks like in all its diversity, but [to] see what sensibilities perhaps women leaders bring to the table. We have different life experiences. We might see different problems. We might see different solutions.”

Gillibrand’s feminism is tightly intertwined with her political biography. When sexual misconduct allegations surfaced against Democratic senator Al Franken in 2017, Gillibrand was the first senator to call for him to go. And while she credits Hillary Clinton with inspiring her to get into politics, that did not stop her from doing something few Democrats dare do in a party still dominated by the former candidate and her husband: say Bill Clinton should have resigned as president over his affair with Monica Lewinsky.

Gillibrand has told Trump to surrender his office as well. That call prompted the president to liken the senator to a prostitute, when he said she “would come to my office ‘begging’ for campaign contributions not so long ago (and would do anything for them)”.

While Gillibrand’s #MeToo criticisms of Democrats had the potential to be politically perilous, her interactions with Trump (and his seemingly sexist response) helped raise her profile. Some have dubbed her “the #MeToo senator”, but other themes are emerging.

Speaking on Saturday at her alma mater, Dartmouth College in Hanover, Gillibrand highlighted her success in traditionally conservative areas of New York, pitching herself to voters as a candidate who could win over Republicans and independents to ensure victory in the general election – and then work across the aisle in Washington.

“To win this campaign,” she said, “you’re going to need to bring together this country, you’re going to need to heal this country, you’re going to need to speak to people in red places and purple places about their lives, about their challenges, about their fears and about what are the right solutions in this country.

“I won back a lot of Trump counties that Hillary lost in New York state alone. I do well in our red and purple districts in my state and win them with higher margins than any Democrat, higher than President Obama, higher than Hillary Clinton, higher than our governor, higher than other senators from New York.”

After mentioning that she had worked with the staunchly conservative Texas senator Ted Cruz, Gillibrand exclaimed: “I can work with anybody!”

‘Success in red and purple districts’

At a Concord coffee shop on Friday morning, Gillibrand approached Tomi Salzmann, a 60-year-old conservative voter, to introduce herself. Asked by the Guardian for her impression, Salzmann said: “Do you want to really know what I think? If she was pro-life I would vote for her.”

Gillibrand campaigns and shops at Hilltop Consignment Gallery in Concord. Photograph: Brian Snyder/Reuters

The first elected post Gillibrand won was a congressional seat in a notoriously conservative area of New York (where cows outnumber Democrats, in Gillibrand’s telling). She was advised that she would not be able to win it. She did.

Her stances then were markedly more conservative than they are today: she had an A rating from the National Rifle Association and had pushed hardline stances on immigration.

Her views have shifted left. On Saturday, she attacked the NRA and gun manufacturers while denouncing the “hatred and darkness” Trump has promoted in talking about immigration.

Her potential appeal to conservative and independent voters was a drawing point for Lili Stern, a 19-year-old Dartmouth student from Dallas.

“I thought she was composed, energised, definitely has the kind of character that can win an election,” she said. “And hearing about her success in red and purple districts and areas was also a plus.”

Olivia Nadworny, also 19, liked the senator’s commitment to bipartisan action.

“It was actually very encouraging and inspiring to hear how she does reach across the aisle and make those connections to people who are different from herself,” she said.

Sue McCoo met the senator when she visited a consignment shop she owns in Concord, buying a small plate with the Lord’s Prayer inscribed on it and a vase for a friend she was staying with. McCoo said she was excited by the number of female candidates, but worried that the rush could hurt their chances overall.

“It’s past time” for a woman president, she said. But “having that many will perhaps mean that in New Hampshire anyways a man will win simply because there are so many women and only so much money and only so many women votes.”

Asked what she is looking for, McCoo said: “It would be nice if it was somebody who was not so extreme that they can’t work with people who totally disagree with them.”