Kevin Sheekey, Michael Bloomberg’s campaign manager, on Thursday said Sen. Bernard Sanders of Vermont had a “great night” at Wednesday’s debate and that the race for the 2020 Democratic presidential nomination could effectively be over soon.

“I don’t think anyone slowed down Bernie Sanders — I think Bernie had a great night,” Mr. Sheekey said on MSNBC.

He said he’s “not sure” whether Mr. Sanders, the current front-runner in national polling, can be caught.

“There is a real possibility, because California is so big and so early in the schedule this year, that Bernie racks up a lead in that state on Super Tuesday that, quite frankly, is just uncatchable,” he said.

“I think we may know a lot about this campaign very early. It may be that there’s not much of a campaign in March after that day, but we’re certainly fighting as hard as we can to make sure that there is,” he continued.

Mr. Bloomberg, a billionaire, was a main target on Wednesday at his 2020 debate debut in Nevada, taking incoming fire on issues ranging from allegedly sexist comments to tough policing policies he championed as mayor of New York City.

“I think he’s got his legs underneath him,” Mr. Sheekey said. “I welcome them for the Bronx cheer they gave us last night, but I think Mike will be back and I think this is a campaign that right now is just getting interesting.”

He said 70% of the party needs to “wake up and realize that we’re heading for a real problem here.”

“We have an existential question, which is what nominee do we want to put before the voters in November to take on this president?” Mr. Sheekey said.

Mr. Bloomberg isn’t competing in the first four states, hasn’t won any delegates to the Democratic National Convention and missed out on the first eight Democratic presidential debates.

Instead, he’s bombarded the airwaves with positive TV ads since entering the race in November.

Still, his team put out a memo before the debate saying the contest is effectively a three-candidate race between Mr. Bloomberg, Mr. Sanders and President Trump.

Sen. Amy Klobuchar of Minnesota took exception to that line of thinking at Wednesday’s debate in Las Vegas.

“I’ve been told many times to wait my turn and to step aside,” she said. “And I’m not going to do that now, and I’m not going to do that because a campaign memo from Mayor Bloomberg said this morning that the only way that we get a nominee is if we step aside for him.”