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Indeed, the group emerged as an antagonist of entrenched centrist Democratic leadership by primarying members like former Rep. Joe Crowley, the then-chair of the House Democratic Caucus, in the Bronx district now represented by Ocasio-Cortez.

Those threats emanate from Donald Trump’s sardonic musings about “primarying” Republicans who cooperate with Democrats.

“That’s a red flag when your head of government is primarying her own party. It is an indication that the ideologies are becoming more extreme,” said Kelly Shaw, the former nonpartisan mayor of the town of Indianola who now teaches political science at Iowa State University.

Mrs. Maloney and Mr. Nadler found themselves primarying one another this election cycle, after 30 years of serving together as political allies in Congress, because a court-appointed special master re-drew parts of their original districts into one Manhattan district.

In an interview with The New York Times, Ms. Biaggi said Mr. Maloney is poised to say she is “hurting the party” by primarying him.