“There can be radical shifts, particularly in Iowa, over the last few weeks” of a campaign, said Patrick Murray, the director of the Monmouth University poll.

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That’s particularly true this year, when there is an uncommonly large group of Democratic candidates — four of whom are bunched together at the top of the field. In most national polling averages, Mr. Buttigieg is at the bottom of that tier, behind former Vice President Joseph R. Biden Jr. and Senators Bernie Sanders and Elizabeth Warren.

All nine of the D.N.C.-sanctioned polls that came out since the last debate were conducted nationally, not at the state level. In such a crowded primary, with months to go before most nominating contests, the national electorate’s preferences are very much subject to change.

Besides, Mr. Murray said, most voters “are going to be facing a very different set of candidates than the ones that are on the ballot right now, because the field will get winnowed down significantly after the February contests.”

“So the polls simply give you a sense of who Democratic identifiers think might be a good nominee, but are in no way predictive of how this process will roll out,” he added.

Indeed, in national as well as state surveys, most Democratic voters still say they are open to choosing a different primary candidate. In a CNN poll released on Thursday morning, 61 percent of Democratic voters nationwide said they hadn’t yet settled firmly on a candidate. That’s compared to 58 percent who said so in CNN’s November poll.