Tepid elite support and Mr. Buttigieg are not Mr. Biden’s only challenges in Iowa. He also has little support from political activists. This has contributed not only to his financial deficit but also threatens his support in a relatively lower-turnout environment like a caucus. Mr. Biden was a distant fourth in Upshot/Siena polling, with 13 percent to 14 percent of support among voters who were “almost certain” to attend the caucus or those who had attended before.

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All of this is separate from another question: whether Mr. Biden’s performance on the stump and on the debate stage is strong enough to retain his support as voters tune in more intensively. Mr. Biden’s resilience in the polls to this point suggests that these concerns could be overstated, though he does seem to have lost more ground in Iowa, where voters are generally paying more attention than they are nationwide. Of course, it is possible that Mr. Buttigieg’s rise, not Mr. Biden’s performance onstage, is primarily responsible for the weakening in his support.

Mr. Buttigieg’s gain might also come at the expense of another candidate: Ms. Warren, who also appeals to the meritocratic-minded, well-educated voters who tend to admire Rhodes scholars or Harvard law professors.

Image Bernie Sanders in Council Bluffs, Iowa. He has outraised all his opponents so far. Credit... Nati Harnik/Associated Press

Ms. Warren’s rise in the polls has been impressive, but there is no reason to assume it will be durable. In Iowa, 78 percent of her supporters said they could change their mind, more than with any of her top rivals, according to the Upshot/Siena poll.

She has vulnerabilities of her own, and she has come under greater scrutiny since she began to match Mr. Biden in national surveys. Her position on “Medicare for all” funding has given her rivals an avenue to attack, and her standing in national and state polls has seemed to slump over the last month.

Her rivals could also point to questions of electability: Although there is still a long way to go, state and national polls show her underperforming her top rivals in matchups against President Trump.