Until Wednesday night, the campaign’s theory of the race seemed to be playing out, buttressed by hundreds of millions of dollars in ad spending and a message that the former mayor has the experience and tenacity to send Democrats back to the White House.

While allowing that the debate had done him little good, Mr. Bloomberg’s advisers were less certain that it had helped others also hoping to appeal to more moderate and independent voters, like Pete Buttigieg, the former mayor of South Bend, Ind., Senator Amy Klobuchar of Minnesota and former Vice President Joseph R. Biden Jr.

Some Bloomberg advisers said it was a conscious choice to largely refrain from attacking anyone besides Mr. Sanders at the debate, reasoning that the Vermont senator is on the cusp of an unstoppable breakthrough if he wins in Nevada on Saturday and has a strong finish in South Carolina a week later.

“We appear to be the only campaign that sees that Bernie is poised to capture the Democratic nomination on Super Tuesday,” said Kevin Sheekey, Mr. Bloomberg’s campaign manager. “I’m not sure if there’s a difference between seeing that too late and acquiescing.”

Mr. Bloomberg’s top strategists are among many Democrats who have invoked the 2016 Republican nominating contest as a cautionary tale. With a front-runner, Mr. Trump, whom some in the party initially found unacceptable, multiple candidates pummeled each other as they fought to position themselves as the surviving non-Trump alternative. And by the end, none were left standing as the party gradually coalesced around Mr. Trump as its nominee — a scenario many swore they could never allow to happen.

In Utah, Mr. Bloomberg suggested that Mr. Sanders, his “hand-waving and finger-pointing” rival, was running a campaign based on reckless, empty promises.

Responding generally to attacks on Thursday, a Sanders spokesman, Mike Casca, said the senator’s opponents “have thrown everything they can at him” since the beginning of his campaign, to little effect.