When New York Democrats emerged from the scrum of redistricting two years ago with a map that largely did not tilt in their favor, there was one spot of consolation: a Republican-held district in Central New York that was redrawn broadly to the Democrats’ benefit.

The first-term incumbent there, Representative Brandon Williams, was already facing a dogfight: He had prevailed in 2022 by fewer than 3,000 votes.

But Mr. Williams has now become a distinct underdog in his new district, one that President Biden would have won by 11 points in 2020.

Mr. Williams, a conservative Republican who has praised former President Trump and celebrated the overturning of Roe v. Wade, is the only House Republican whose race is listed as “lean Democrat” by the Cook Political Report.

As Election Day draws closer, the increasingly personal race between Mr. Williams and his Democratic challenger, State Senator John Mannion, in New York’s 22nd Congressional District remains critical for both parties, with the balance of the Republican-led House in play.

Mr. Williams has received help from the National Republican Congressional Committee and the Congressional Leadership Fund, which the ad tracking firm Ad Impact says plan to spend more than $3 million on ads painting the moderate Mr. Mannion as dangerously liberal on issues like immigration and crime (one of them features John Walsh, the creator of “America’s Most Wanted”).