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“The Democratic leadership would probably rather have him resign than stick around and embarrass the Democratic Party brand,” Mr. Bonjean said.

“He’s basically a walking black hole. Everybody wants to stay away from him and not get sucked into the mess.”

A slim majority of New Yorkers say Mr. Weiner should remain in office, though a larger majority say the lawmaker should give up aspirations of running for mayor, a new poll says.

A NY1-Marist Poll survey conducted hours after Mr. Weiner admitted to sending the lewd photo on Twitter showed that 51 percent of New York City voters said Mr. Weiner shouldn’t resign from Congress, with 30 percent said he should step down. Eighteen percent said they aren’t sure.

But when it comes to the 2013 race for New York City mayor, 56 percent said they don’t want him to make a bid for the office, including a majority of Democrats, the poll says.