Representative Kathleen Rice, Fourth District (Long Island)

Potential challenger: Kevan Abrahams, a Nassau County legislator

Ms. Rice opposed Representative Nancy Pelosi’s election as House speaker and has not embraced the “Green New Deal,” a progressive proposal to fight climate change. Mr. Abrahams narrowly lost to Ms. Rice in 2014.

Representative Yvette Clarke, Ninth District (Brooklyn)

Potential challenger: Adem Bunkeddeko

Ms. Clarke narrowly defeated Mr. Bunkeddeko in 2018, when he argued that she was insufficiently progressive. She said that she was better prepared now to serve constituents and get her message out.

Representative Jerrold Nadler, 10th District (Manhattan, Brooklyn)

Potential challenger: Lindsey Boylan, a former adviser to the governor

Mr. Nadler, 71, has been in Congress for 27 years. Ms. Boylan said, “I just can’t justify having my daughter watch me sit on the sidelines.”

Also, Mr. Nadler, the House Judiciary Committee chairman, has resisted opening a formal impeachment inquiry for President Trump. Now the congressman is the target of a $200,000 ad blitz from a California billionaire who supports impeachment.

Representative Carolyn B. Maloney, 12th District (Manhattan, Queens)

Potential challenger: Suraj Patel

Ms. Maloney, 71, who has been in Congress for 26 years, defeated Mr. Patel last year by a narrower percentage than was customary for her, suggesting vulnerability. Mr. Patel argued that Ms. Maloney had been in office too long and accused her of being “recklessly indifferent to the less privileged.”