By 4am on Monday morning Amy Klobuchar was headed to the airport to catch a flight from Iowa, where she packed a dizzying six campaign events into a 36-hour window, back to Washington DC, where her presence was required at the US Capitol for day six of the Senate impeachment trial of Donald Trump.

As soon as the proceedings in the Senate finished for the day, shortly after 9pm, the Minnesota senator dialed into a “tele-town hall” with Iowa voters.

“I never thought that I wouldn’t be there with all of you,” she said on the conference call. “I hope you understand that.”

Such is the life of a US senator running for president while on jury duty for an impeachment trial, only the third in American history. Instead of barnstorming Iowa’s 99 counties in the final days before the caucuses on 3 February, she is locked up in a room for hours on end with 99 other senators – three of whom are also running for president.

For the next several days and possibly weeks, as the Senate grapples with the thorny question of whether to call witnesses, and ultimately moves to a vote on whether to remove the president from office, Klobuchar and her colleagues Senators Bernie Sanders of Vermont, Elizabeth Warren of Massachusetts and Michael Bennet of Colorado must continue to balance their “constitutional duty” with their responsibilities as a presidential candidate at a critical moment before voting begins.

The rules of the trial effectively prohibit double-duty: senators must be in their seats six days a week. No cellphones. And absolutely no talking, archaically but loosely enforced on “pain of imprisonment”.

The situation has forced the Democrats to get creative about how they campaign from hundreds of miles away, in a state where voters famously like to meet their candidates before making a decision.

While the senators are holding town halls by phone and video, dashing to TV hits during trial breaks and chartering last-minute flights timed to the crack of the gavel concluding the day’s session, two of their top rivals, Joe Biden and Pete Buttigieg, crisscross Iowa on dueling bus tours.

“Even though this race has been going on for some time and voters know the candidates by now, there is still nothing like having the candidate there to rally the troops in that last week,” said David Redlawsk, a political scientist and author of Why Iowa: How Caucuses and Sequential Elections Improve the Presidential Nominating Process.

In their stead, the senators have dispatched a range of high-profile supporters such as the New York congresswoman Alexandria Ocasio-Cortez (Sanders) and former housing secretary Julián Castro (Warren) as well as lesser-known family members, local officials, activists and even an Olympic curling coach (Klobuchar).

This week, Warren’s husband, Bruce Mann, will travel across Iowa on her behalf with their golden retriever, Bailey, while Sanders’ wife, Jane, will stand in for him at a rally and concert. And Klobuchar’s daughter, Abigail Bessler, last week kicked off the first in a series of locally hosted “Hotdish House Parties”.

Less than a week away from the caucuses, the race is bunched so tightly at the top that even the smallest changes could have an impact. Polling shows an unusually large share of Democrats are still uncommitted, overwhelmed by the historically large field and gripped by a fear of nominating a candidate who can’t beat Trump. A recent Monmouth University poll found that nearly half of Iowa voters could change their minds before the caucuses.

Andrew Yang, a tech entrepreneur and dark horse presidential candidate, joked at a Bloomberg News reporter roundtable in Des Moines on Wednesday that campaigning in Iowa “every weekday for the two weeks before the caucuses” should be the “decisive criterion” for support.

Striking a more serious tone, Yang said his rivals clearly faced a “disadvantage” by not being in the state.

“Imagine knowing you want to be in Iowa talking to voters, furthering this campaign that you’ve been working towards in many cases for years or decades, and you’re not here,” he said. “I feel terrible for them.”

Even before the trial began last week, it was transforming the race in other ways.

At the heart of the trial are revelations that Trump solicited help from Ukrainian officials to damage Biden, the Democratic frontrunner. Trump and his legal team have repeatedly accused the former vice-president without evidence of seeking to remove a Ukrainian prosecutor who was investigating Burisma, a natural gas company that employed his son Hunter Biden while he was in office.

Senator Joni Ernst, a Republican from Iowa, told reporters after a presentation by Trump’s defense team that centered on Hunter Biden that she was “really interested to see how this discussion today informs and influences the Iowa caucus voters”.

“Will they be supporting Vice-President Biden at this point?” she asked.

At his events this week in Iowa, voters said the allegations – which most believed to be baseless – would not dissuade them from voting for Biden. But there were some who voiced concern that the accusations could cast a cloud over Biden’s candidacy the way the email scandal hurt Hillary Clinton in 2016.

Biden, who has highlighted his electability as an asset against Trump in a general election, cited Ernst’s as proof that the president fears running against him.

“She spilled the beans,” he told voters at a campaign stop in Muscatine on Tuesday. “The whole impeachment trial for Trump is just a political hit job to try to smear me because he is scared to death to run against me. And he has good reason to be concerned.”

With the caucuses days away, the senators have stepped up their outreach from afar.

The Sanders campaign has leveraged his massive social media following with livestreamed events and a new video published on Tuesday that responds gleefully to the mounting concerns from within the Democratic party that the Vermont senator could actually win the caucuses, if not the nomination.

Warren on Tuesday hosted a tele-town hall. More than 20,000 Iowans participated, according to her campaign.

The timing is especially inconvenient for Klobuchar, who has staked her campaign on a strong performance in Iowa. Though she lacks the financial firepower or national prominence of Sanders and Warren, her campaign has showed signs of strength in recent weeks, earning a handful of high-profile endorsements from regional and national editorial boards and is climbing in some recent polls.

“We’re seeing a lot of momentum for our campaign just when I can’t be there,” Klobuchar said to the more than 11,000 people who dialed in to the call, according to her campaign. Before signing off for the night, she implored them that an upset in Iowa was within her grasp.

“Every sign is that I can,” she said. “I just need you to help me make that extra, extra, extra push.”

But Klobuchar was leaving nothing to chance.

After an unexpectedly early close to Tuesday’s proceedings, Klobuchar slipped out of the Capitol and on to a flight bound for Council Bluffs.