The survey is full of alarming signs for Mr. Biden, who entered the race in April at the top of the polls in Iowa and nationally. He is still in the lead in most national polls, but his comparatively weak position in the earliest primary and caucus states now presents a serious threat to his candidacy. And Mr. Biden’s unsteadiness appears to have opened a path in the race for other Democrats closer to the political middle, particularly Mr. Buttigieg…

Factoring in voters’ second choices, which can play a key role in the complex caucus process, Ms. Warren had the broadest appeal: She is the first or second preference of 47 percent of Iowa Democrats, with two-thirds of Sanders supporters naming her as their backup choice.

Mr. Sanders is the first or second choice of 34 percent of likely caucusgoers, followed by Mr. Buttigieg at 31 percent. Mr. Biden was in fourth place by this measure, at 28 percent; only 1 in 10 voters named him as their second choice.