Hempstead Town Supervisor Kate Murray has also had her name mentioned as a prospect to succeed McCarthy in the media and elsewhere. Hempstead officials did not return calls for comment.

Candidates can begin collecting signatures on ballot petitions in March, and party primaries will take place in June. Democrats have a slight enrollment advantage in the 4th District, and McCarthy won election nine times, but Republicans held the seat for decades before McCarthy, and many are predicting that Democrats will lose ground in the House of Representatives, where they are already the minority, in 2014. Prior, Silverstein and Scaturro all predicted that backlash to President Obama’s performance, including his signature healthcare law, would hurt Democrats and favor Republicans in November’s election. The president’s party often loses congressional seats in midterm elections.

As this race is likely to draw political donations from beyond the district, a key factor in who becomes his or her party’s nominee will be candidates’ fundraising abilities.

Phillips said Rice would be the Democratic Party’s most viable candidate, if she decides to run. “There’s no doubt that she has the most experience, the highest approval rating and the most extensive financial supporter network of anyone who may be in the field,” he wrote in an email. “If her decision is to run, we’d be extremely confident in both a primary and a general election.”

Becker said he has already begun the “preliminary work” of “reaching out to people to see if I can get the financial support.”

Denenberg said he is considering multiple factors as he mulls a run for Congress or state Senate. “I’m looking at where I can better serve my constituents and the constituents of these larger districts and make a greater positive difference, whether it’s Albany or Washington at this point,” Denenberg said.

Mary Malloy and Emily Webb contributed reporting.