At beachfront hotel bars, tropical pool parties and crowded ballroom dance floors, a pressing matter closer to home inevitably arose: How would New York City navigate four years of Donald J. Trump as president, and who might be the best mayor to lead that effort?

At the political conclave known as Somos, the need to battle a Trump administration offered some room for consensus for the five Democrats running to unseat Mayor Eric Adams in next June’s primary.

So did another shared view: Neither Mr. Adams nor another rumored candidate, the former Gov. Andrew M. Cuomo, deserved the support of voters.

“One of the things that absolutely unites us is a clear opposition to disgraced New York executives, whether that is Adams or Cuomo,” said Zohran Mamdani, a state assemblyman from Queens and mayoral candidate.

Mr. Adams and Mr. Cuomo were not in attendance. Mr. Adams, a Democrat, had planned to go but canceled his trip late in the week. Three years ago, he relished a rock-star presence at Somos; now the mayor, who was indicted on federal corruption charges in September, has seen his poll numbers sink to record lows.

Critics of Mr. Cuomo are mobilizing to torpedo his potential candidacy after polls showed that he could be a top contender. A group that opposes him released a digital ad targeted to Somos attendees about the sexual harassment allegations that prompted Mr. Cuomo to step down in 2021. Mr. Cuomo has denied wrongdoing.