Mr. Zeldin’s entry into the governor’s race paved the way for Democrats to try and flip his now-open congressional seat in the First District on the eastern end of the island, one of the few Republican-held seats in the country that is open and considered competitive. But Democrats face an uphill battle: The seat is projected to slightly favor Republicans, who have held the district since Mr. Zeldin wrestled it from Democratic control in 2014.

The Democrat in the race, Bridget Fleming, a former assistant district attorney and current county legislator, has nonetheless outpaced her opponent in fund-raising and recently received the endorsement from the union that represents police officers in Suffolk County. She was also added to the Democrats’ Red to Blue program in June.

A moderate, she has centered her campaign in the district, a mix of working-class and wealthy residents, on affordability and conserving the environment — a top issue for fishermen and farmers, as well as the tourism industry, on the island’s East End — but also on protecting women’s right to choose.

“There’s no question that fundamental freedoms are under assault in our country,” said Ms. Fleming. “The exploitation of the extremes that we’ve seen recently is electrifying people who are standing up to fight for themselves.”

In an interview, her opponent, Nicholas LaLota, brushed off Democrats’ almost singular focus on reproductive rights, saying that New York already had some of the strictest protections in the country.

“Here in New York, nobody’s abortion rights are under attack or assault,” said Mr. LaLota, a former Navy lieutenant who works in the Suffolk County Legislature. “So those folks who want to campaign on abortion, they should run for state office, not federal office.”

He added that voters in the district “who live paycheck to paycheck were more concerned about rising interests rates and prices.”

Democrats are facing an even steeper climb to unseat Representative Andrew Garbarino, a well-funded Republican who represents the Second District on the South Shore that is among the most affluent in the country. Opposing Mr. Garbarino is Jackie Gordon, an Army veteran, who lost to Mr. Garbarino in 2020.