“A lot of people have been with Cory and have been supporting him for two decades, and he’s only 50 years old,” said Whitney Tilson, a longtime fan who said Mr. Booker “would surprise everybody” in Iowa because of his high favorability ratings — people who like him but aren’t committed to caucusing for him — in the polls. “He will be president someday.”

At 7:30 p.m. on Friday, on the way to his final event of the day, a fund-raising call with Judy Zamore, his campaign’s chief financial officer, and Addisu Demissie, the campaign manager, revealed the weeklong surge.

“We are about $1,000 shy of having $1.1 million in for the week, that’s pretty amazing for us,” she said. But Ms. Zamore warned that “it is definitely starting to come back to earth a little bit,” and the possibility of missing the debate stage could make it much harder to continue at the current pace.

One key to the Booker campaign’s relative staying power is an extreme dedication to frugality, set by Mr. Demissie and Ms. Zamore. They have staff make their ads in house, instead of hiring an outside consultant. On the road, Mr. Booker regularly stays in supporters’ homes, and has staff do the same. At every all-staff meeting, Mr. Demissie gives out “super saver awards” to especially budget-minded staffers, like those who car-pooled instead of taking a train.

But a tight budget has also significantly hampered the operation. The campaign has still not advertised on television, and only this week began running digital video ads. And while they have a broad staff of organizers on the ground, the campaign has only five field offices in Iowa. As of October, Mr. Buttigieg had 22 field offices across the state.

Difficult Discussions

Though Ms. Young, the pollster, had explained to Mr. Booker that time was running out for him to meet the polling thresholds for the December debate, the candidate was still exploring his options.