Under a recount — a closer level of scrutiny — party officials would conduct a “hand count and audit of Presidential Preference Cards to ensure that caucus votes were tallied and reported correctly in the caucus work sheets and reporting forms,” the party explains.

Mr. Price said on the call, referring to the caucus chairs: “Our guidance to folks was: Everyone needs to hand in their preference cards on caucus evening. We trained folks to do just that.”

Is this likely to change the results?

A recount based on the cards, if it comes to that, might not be definitive in a razor-close race, as now exists between Senator Bernie Sanders of Vermont and Pete Buttigieg, the former mayor of South Bend, Ind. This is the first caucus in which cards were used, intended to act as a paper trail after criticism that the caucuses lacked transparency.

Caucusgoers wrote their first choice on one side of the card, and if that candidate did not reach a threshold of support and was knocked out, the caucusgoer could flip the card over and write in a second choice. The cards were supposed to be turned in to the caucus administrators.

But in interviews this week, a number of caucus chairs said that there were undercounts in the cards they submitted to the state party and the number of people who voted. In other words, not everyone turned in a card.

“We collected 186 cards; four people left without turning in a card,” said Pat Loeffler, who helped run a caucus in Linn County. His precinct, Cedar Rapids 39, reported 190 votes on the work sheet submitted to the party. Mr. Loeffler’s job was to stand at the door. “I was basically asking if they turned in their card or not,” he said, adding that it had been easy for people in a hurry to dart past him.