MUSCATINE, Iowa — The voters, given a rare chance to speak privately to Elizabeth Warren, do not shy away from pointed questions: Can you really beat Donald Trump? Why do you want to kill the private insurance industry?

One voter, an important local official in Iowa, jokingly resurrected a personal grievance, reminding the senator how, as a well-known Harvard law professor, she declined to publish an article in the Iowa Law Review.

Before her town hall meetings, Warren (D-Mass.) virtually always holds a private discussion with five to 40 carefully selected voters, from those who are wavering to potential endorsers. At a moment in the presidential campaign when raucous rallies are the order of the day, the sessions provide unusually intimate access for Iowans who have emerged as the high-value targets of this final, desperate sprint to the caucuses: highly active but still undecided Democrats.

These “clutches,” as the campaign calls them, are just one part of Warren’s obsessively detailed organization in Iowa, one that reflects the candidate’s methodical personality and sets her apart from every other contender. As her polls take an ominous dip just days before the Feb. 3 caucuses, Warren’s big bet is that her unprecedented organizing machine will rescue her showing in Iowa, essentially saving her candidacy.

“It’s been a year of town halls and questions and a lot of selfies — it’s been a lot of fun,” Warren told Democratic officials Saturday at a gala in Scott County. But, she added, “there’s also been a part that’s not quite so visible: It’s been a year of organizing. It’s been a year of people on the ground.” And that, she said, “is how we’re going to win in 2020.”

That “year of organizing” will have its ultimate test in one week.

And it has been almost microscopic. The campaign made a detailed study of almost all of the state’s more than 1,600 precincts to determine how to maximize support. It divided Iowa into nine zones and made an early investment deploying numerous operatives in each one, including remote towns and areas unlikely to support Warren.

To decide whom to invite to her intimate clutches, which last 25 to 30 minutes, the campaign mounted an extensive data-gathering effort to uncover not only who supports her but also who might switch under the right circumstances.

One Warren script, handed out this month to volunteers knocking on doors on her behalf, made that point clearly. “What got you excited about [FIRST CHOICE CANDIDATE] in the first place?” reads the script, which was shared with The Washington Post. “Elizabeth feels strongly about that issue too. . . . After hearing a bit more, is Elizabeth your second choice?”

If the voter says “yes,” the volunteer is instructed to label that person a “prospect,” and they might get invited to a clutch.

Similarly, Warren’s town hall gatherings are populated with some of the voters her organizers have identified as undecided.

For Warren, the bet on Iowa and organization was made long ago. One of her key early decisions was to bulk up fast in the state, hiring 50 staff members by the spring of 2019, far outpacing all other campaigns. Early in the campaign, Warren’s team handed out stickers that read: “It all begins in Iowa.”

It has gotten only more elaborate. In recent weeks, some Warren organizers have touted their successes online, with operatives in Sioux City, Washington County, Jefferson County, Cedar Falls and Council Bluffs announcing that they have precinct captains for every precinct in their jurisdiction. The campaign declined to say how many precinct captains they have identified statewide.

Yet since surging several months ago, Warren is fading somewhat in the polls at an inopportune moment, nationally and in Iowa. The most passionately liberal Democrats appear to be rallying around Sen. Bernie Sanders (I-Vt.), while those favoring a safer, more centrist choice are gravitating toward former vice president Joe Biden.

Warren, who argues that she can appeal to both wings of the party, gained a prized endorsement from the Des Moines Register on Saturday, but she trails Sanders in a recent poll by the newspaper. Nationally, a Washington Post-ABC News poll shows Sanders and Biden gaining strength, while Warren has fallen to 12 percent from 23 percent in October.

Warren officials appear to be lowering expectations for Iowa. Campaign manager Roger Lau issued a memo Friday warning against “breathless media narratives” emerging from the caucuses.

In the same memo, Lau played up Warren’s organization, noting that she has more than 1,000 campaign staff members nationwide and has held “over 100,000 one-on-one conversations” during the campaign so far.

It’s the campaign’s hope that this sort of detail and personalized attention will overcome the passion surrounding Sanders and the goodwill surrounding Biden, two much more improvisational and less organized candidates.

“Whether or not that individual attention will translate on caucus night is anyone’s guess,” said Elesha Gayman, the Scott County Democratic chair, who has not endorsed a presidential candidate. “But that’s her strategy — she’s trying to get one-on-one with voters as much as she can.”

One example came Saturday afternoon, just after Warren and her team flew from Washington — where she was attending President Trump’s impeachment trial — to Iowa for an afternoon town hall event at a school in Muscatine, a town on the banks of the Mississippi River.

As a Warren organizer gave a brief speech to warm up the crowd, Warren was in a classroom, standing in front of a whiteboard and taking questions from a hand-selected group. Then the participants stood for a photo with her, allowing them to skip the longer photo line later.

“It feels good,” said Deb Owen, a Warren volunteer who is providing housing to two campaign staff members and was invited to the smaller session. “You’re in the room with her, and you feel like you can have a conversation and you’re not just a face in the crowd.”

The goal, said one Warren ally familiar with the strategy, is to give voters and volunteers the kind of treatment that campaigns typically reserve for big donors.

“They are the core of the organization,” Kristen Orthman, Warren’s communications director, said of the volunteers who are invited to the meetings. “They are the people Elizabeth and our team can count on to make the case and win support to our corner on caucus night.”

Still, the clutches — plus the long photo lines after every event in which attendees can take their own selfies — mean Warren’s town hall meetings take a lot of time. Perhaps as a result, she, along with Biden, has held the fewest individual Iowa events of any of the major Democratic candidates.

According to the Des Moines Register’s candidate tracker, Warren has held 98 campaign events over the past 58 days, and Biden has held 99 over the past 51 days — although he began a 21-stop bus tour of the state on Sunday. By contrast, Sanders has held 132 events, and Sen. Amy Klobuchar (Minn.) has held 181 over roughly the same period.

Meanwhile, the Trump impeachment trial is creating last-minute obstacles for Warren’s strategy. In one conservative-leaning rural area, Warren organizers and supporters recently identified several undecided voters and arranged for them to meet the senator. But the trial schedule prevents in-person meetings, so Warren instead has been calling the voters individually, according to a supporter who spoke on the condition of anonymity to discuss internal strategy.

Warren’s team has about 150 organizers in Iowa, according to the campaign. Although that is no longer the biggest footprint, Warren’s advantage comes from being here early.

In urban areas, her team assigned one organizer to a single county, while in rural regions, each organizer oversaw two or three counties at most. Meanwhile, staff members for other candidates were sometimes assigned as many as a dozen counties, a tough job in rural parts of the state where Democrats are often spread out and meeting them requires long drives.

“I think the Warren campaign smartly decided very early on that turf like that is not how you build relationships,” said one Iowa Democrat. “You can’t get to know people in a real way if you’re driving three or four hours or more every day.”

Although Pete Buttigieg, the former mayor of South Bend, Ind., is employing a similar type of one-on-one organizing, Democrats not affiliated with either campaign say Warren’s organizers have simply been at it longer. And they’ve often been deft at how they go about it.

When Sen. Kamala D. Harris (D-Calif.) left the presidential race in December, for example, Warren’s team hired a group of her former organizers and had them call former Harris supporters to ask them to join Warren’s team.

Still, all this attention to detail has not defused the biggest question Warren faces as a candidate. Organizers mounting door-to-door efforts or reaching out to voters in remote locations regularly hear questions about whether she could beat Trump.

It’s a challenge that has come up in urban, relatively liberal cities such as Des Moines and Cedar Rapids, where voters often sound like pundits when approached by canvassers — asking how gender might play among working-class voters in battleground states such as Michigan and Pennsylvania.

But it also arises in more rural, conservative areas such as northwestern Iowa.

“When I knock [on] doors, they all say, ‘Oh, I love Elizabeth. She has the best plans, and I think she’d be the best president. But I don’t know if she can win,” said Peter Leo, chairman of the Carroll County Democrats, who endorsed Warren last fall. “My hurdle as a volunteer for her has been to convince people to go with that gut feeling that Elizabeth Warren is the president that we need.”