Large numbers of Iowans traditionally break for a candidate in the last week; this year, with four candidates knotted up at the top, many voters are not expected to decide until caucus night. The Buttigieg campaign’s ground game is designed to present undecided caucusgoers who enter their precincts with tightly knit cells of Buttigieg supporters. The campaign’s national caucus director, Travis Brock, has toured the state training more than 1,000 people to assume leadership roles in their precincts.

“We know there’s going to be a sizable portion of people who walk in undecided on caucus night, and they’re going to want to see a well-organized, enthusiastic group who can persuade you,” said Brendan McPhillips, the campaign’s Iowa director.

Voters at Buttigieg rallies in recent days said they were weighing between him and Mr. Biden, between him and Senator Amy Klobuchar, between him and Ms. Warren — even between Mr. Buttigieg and Mr. Trump.

Josh Heard, a Buttigieg caucus precinct leader, said canvassing his neighborhood in Council Bluffs was like herding cats. “A lot of them will say, ‘I support Pete,’ and I’ll come back around the next time and there’ll be a Biden sign in their yard,” he said.

The former vice president has a commanding lead among black voters nationally, especially older voters, but if Mr. Biden falters — including if the impeachment trial renews scrutiny of his conduct in Ukraine and harms his standing — black voters will seek an alternative, the Buttigieg campaign believes.

At a forum in Des Moines on Monday aimed at voters of color, Mr. Buttigieg was pressed about a new wrinkle in his management of the police in South Bend, which has roiled his candidacy since the summer. He was asked about a report that black officers had unsuccessfully sought a meeting with him to air grievances.

“I’ve had countless meetings with officers, including officers of color,” Mr. Buttigieg replied, noting that some of those reaching out faced accusations of misconduct or were threatening lawsuits. “When someone threatens to sue you, you make sure they’re talking to a lawyer,” he said.