Liuba Grechen Shirley, a Democratic activist challenging a longtime Republican incumbent, Representative Peter King, is among the wave of women inspired to run by the election of Donald Trump. She previously helped galvanize Democrats and women in the district by starting an organization to oppose the Trump agenda, particularly the attempted repeal of the Affordable Care Act. When Mr. King voted to end that law, she first protested as a constituent, then decided to run against him.

Ms. Grechen Shirley has a professional background in global development, working for the United Nations Foundation. That she is also a mother of two young children won her national attention this year when she persuaded the Federal Election Commission to let her spend campaign funds on child care, making her the first woman to do so.

She supports Medicare for All, a federal minimum wage of $15 per hour and expanded funding for prekindergarten programs. She would also extend Temporary Protected Status to immigrants who fled disaster at home. That more welcoming approach would be a much needed change from Mr. King, who supported Mr. Trump’s so-called Muslim travel ban. Mr. King has also stirred anti-immigrant sentiment more generally, in his district and nationally. Asked about the separation of children from parents at the border, he told one news outlet: “Americans care more about Americans.”

Mr. King has served in Congress since 1993, but, with Democrats energized, Ms. Grechen Shirley has a path to victory.

New York’s First District, Long Island.

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Like most campaigns this fall, this one has focused on what Congress can do, not what the White House has done. Perry Gershon, the Democrat, supports Medicare for All and has backed the Affordable Care Act, which the Republican incumbent, Representative Lee Zeldin, voted to gut. Mr. Gershon, who wants to discuss sensible restrictions on immigration, has backed protection for Dreamers without other stipulations, unlike Mr. Zeldin. Mr. Zeldin supports withdrawal from the Paris climate agreement, which could have dire consequences for district with miles of coastline.

But the president has had a cameo part in the race. Mr. Gershon has provocatively said he was inspired to run by seeing parallels between Hitler’s rise and Mr. Trump’s rise while visiting the United States Holocaust Memorial Museum in Washington. Mr. Zeldin, who has enthusiastically backed Mr. Trump, kicked off his re-election campaign at an event with Sebastian Gorka, a far-right former Trump aide who has worn a pin from a Hungarian group founded by Nazis. That group has claimed Mr. Gorka as a member, although he denies it. Mr. Zeldin has also had a fund-raiser with Steve Bannon, another former Trump aide, who has been connected with some of the most extreme right-wing groups in Europe and the United States.