Amy Klobuchar was running on 3½ hours of sleep when she arrived at a downtown Washington television studio. Between spritzes of hair spray and sips of coffee, she was trying to remember how many campaign trips she had taken to New Hampshire. Was it 22?

The next one would have to wait. As a senator, Klobuchar had been on jury duty in President Trump’s impeachment trial until nearly 2 a.m. and was due back in the Capitol soon for another marathon session. This was far from ideal for her other full-time job: candidate for the Democratic presidential nomination.

Never before has anyone attempted what Klobuchar and three of her colleagues are trying to pull off — balancing historic responsibilities in Washington with trying to deliver closing arguments to voters in Iowa before balloting begins there Feb. 3, and in New Hampshire, which votes just eight days later.

“I have my job to do. And the chips will fall where they may,” Klobuchar said in an interview, dismissing the uncertainty that has been injected into her candidacy.

For Klobuchar (D-Minn.) and Sens. Bernie Sanders (I-Vt.), Elizabeth Warren (D-Mass.) and Michael F. Bennet (D-Colo.), the timing of the trial — just the third in U.S. history — could hardly be knottier. Running six days a week, it has forced them to cancel events, spend hours on end without access to their smartphones — banned during the trial proceedings — and remain hundreds of miles away from the early states where they had once planned to spend much of January.

It has been particularly challenging for Klobuchar, who entered the race as a solid, if not overwhelming, contender, respected within the party in Washington and hoping to offer Iowa the option of a get-things-done Midwestern centrist.

Since entering the race Feb. 10 — in a blizzard, which earned her the tweeted sobriquet “Snowman(woman)” from Trump — she has pitched herself as the best candidate to win back the voters who sided with him in 2016.

“There’s a lot of people talking the talk — but I actually bring the receipts,” she told a woman from Grimes, Iowa, during a telephone town hall on Wednesday night from Washington.

“I can unite our party. . . . I think that is going to be key.”

For months, however, her candidacy has been eclipsed by the presence of former vice president Joe Biden and former South Bend, Ind., mayor Pete Buttigieg, similarly selling themselves as pragmatists on the moderate end of the party’s ideological scale.

She lately has tried to push into the top tier of candidates with some high-profile endorsements and well-received performances, including in the most recent debate in Des Moines.

But any momentum has been threatened by the demands of being present for the impeachment trial in Washington at the same time that Iowa’s legions of undecided voters are coming to a judgment.

Unlike her better-financed rivals, who have raised tens of millions of dollars to organize in states farther down the campaign calendar, Klobuchar’s future is almost wholly dependent on how she does in Iowa. So, she finds herself most every moment she is not in the impeachment trial seeking to reach voters there through television interviews, video conferences and telephone town halls, all beaming her in electronically.

At around 10 a.m. Wednesday, Klobuchar was in a TV green room at Hearst Television in Northwest Washington, preparing for three consecutive interviews with early-state television stations. She had already joined a video chat that morning with a group of Democrats living outside the United States, who will begin voting March 3. The Senate trial started in earnest on Tuesday at 1 p.m. and did not adjourn until Wednesday at 1:49 a.m., leaving little time for sleep.

As a stylist put some finishing touches on Klobuchar’s hair, her national press secretary, Carlie Waibel, briefed her on what was coming. First up: a Des Moines station and a reporter she had spoken to before.

“I think the biggest topics are going to be [a] kind of state of the race; we’re two weeks out,” Waibel said. “Then impeachment — specifically, what you have going on the ground in Iowa while you’re here. And then of course your thoughts on the first day.”

Klobuchar, a former prosecutor, had her talking points down. “Zero witnesses and zero documents equals zero justice,” her voice deepening as she took Senate Republicans to task for not holding a more expansive trial. “C’mon, three hours’ sleep,” she added proudly.

“Bring it,” Waibel responded with a laugh. She told Klobuchar that she would also be speaking with stations in Boston and Manchester, N.H.

“We have been there 22 times?” Klobuchar wondered aloud as she asked for her coffee cup. She asked an aide to find out and to get her New Hampshire state director, Scott Merrick, on the phone. “Twenty-one,” replied the aide, before handing the phone to Klobuchar. She put him on speakerphone, and he briefed her on the campaign’s surrogate activity.

“How about that gold medal curling champion?” Klobuchar interjected, referring to Phill Drobnick, a former Olympic coach who is campaigning for her. “He’s in Iowa this week, but I’m telling you, I think he could be really popular in New Hampshire.” She added, “I’m in impeachment, we’ve got that guy.”

Then it was on to the interviews.

“I can’t be there every moment like I would like,” Klobuchar told KCCI in Des Moines. “So having people that aren’t just window dressing, that are actually really, really committed to help me,” she added, naming some or her local endorsers, “that just makes a huge difference for me.”

By a few minutes after 11 a.m., Klobuchar was back in the lobby, where a pack of reporters had staked her out. “This is my life right now,” Klobuchar told them, reflecting on the interviews she had just done. “We’re trying to reach people in the early states.”

She faced a question about whether rival candidate Joe Biden’s son Hunter Biden should be brought to testify in exchange for former national security adviser John Bolton. (“Discussions should always go on about a trial,” she said, but “we need relevant witnesses to what happened.”) She talked about being cut off from the outside world during the trial. (“All of a sudden, you’re in like digital detox. You’re sitting in there, you can’t, you know, look at your phone, you can’t communicate, really,” she said.)

“It’s a moment of reflection about why I’m doing this and what our democracy is all about,” Klobuchar said. “And there is a relation here, because this hearing, just like my quest to become president, is about a decency check.”

The senator from Minnesota knows well how news can break in the campaign at any moment, putting a premium on the ability to digest it and react quickly. She was on a flight from Iowa to South Carolina a week ago when she learned that she and Warren had won a joint endorsement from the New York Times editorial board.

“We’re still dealing with all this impeachment stuff and what the schedule is and my speech for South Carolina,” Klobuchar recalled as she rode shotgun in a GMC Terrain to her next round of interviews in Washington. ­Waibel, who was on the flight with her, had gotten some texts and alerted Klobuchar that she was a finalist.

“She goes, ‘It’s down to two.’ And then two minutes later, she goes, ‘They might endorse two,’ ” Klobuchar said.

That grabbed the senator’s attention.

For a moment, all of the questions floating around in her mind — including whether she had gloves for the weather in South Carolina — faded away, she said. When it was official, she decided she had to send out a midflight tweet.

“An honor!” Klobuchar wrote.

The SUV rolled to a stop as she finished telling her story. Waibel briefed her on the next two interviews — one with a station in Cedar Rapids, Iowa. She also told Klobuchar that a crew from the Showtime program “The Circus” was meeting her there.

Klobuchar swapped out her New Balance sneakers for a pair of boots and stepped out.

Like every other candidate, Klobuchar is inclined to offer the rosiest picture of her odds in the first, crucial state. She said in an interview with an Iowa station Wednesday morning that she was “surging” in the state. While her poll numbers have improved, some local Democrats said they are not seeing a big increase in support for her.

“I mean, I wish it were true, because I really do like her a lot. But I’m not seeing her upswell,” said Sean Bagniewski, the chairman of the Polk County Democrats in Iowa. (On Saturday, the Des Moines Register gave its endorsement to Warren.)

After her interviews, Klobuchar returned to her apartment briefly before traveling to the Capitol. As the trial recommenced, Klobuchar took a seat at her desk in the back row, between Sens. Robert P. Casey Jr. (D-Pa.) and Christopher A. Coons (D-Del.). She took some notes as Rep. Adam B. Schiff (D-Calif.) presented his case against Trump. Within the first 45 minutes, she and Coons passed notes back and forth.

During a midafternoon break, some senators milled about outside the chamber, fielding questions from reporters. Klobuchar made a beeline to the other side of the Capitol, where she did an interview with CNN. During a later intermission, she went on MSNBC.

The proceedings ended at 9:42 p.m., but Klobuchar still had campaigning to do. In her campaign’s D.C. workspace, aides had set up the telephone town hall so Iowans could dial in and ask her questions. “I’m just off the Senate floor,” she said on the call.

“I’m going to be there again tomorrow, and the next day and the next day,” she said. “Which is why we’re doing this tele-town hall.” Her family, she said, has been in Iowa, campaigning in her place.

The next morning, Klobuchar was back in the campaign workspace for an editorial board meeting with a New Hampshire newspaper group. Seated at a conference table in front of an Apple laptop propped up on a stack of books, she fielded questions on video.

“I thought our schedule would be such that I could have come up to do this,” she told them. “But such is life. We’ll just adapt.”

Her campaign has searched for creative ways to generate excitement in her absence. On Friday, as senators settled in for another long day in the Capitol, Klobuchar’s daughter, Abigail Bessler, held a “Hotdish House Party” in Iowa City. Former Olympic coach Drobnick visited curling club on her behalf in Des Moines.

After one of the Senate’s longest weeks in recent memory, its Saturday session finally ended at 12:01 p.m., prompting the presidential hopefuls to sprint back to the campaign trail, knowing that they would need to return Monday.

As she left the Capitol, Klobuchar sounded triumphant when reporters asked if she was excited to be headed to Iowa.

“I am! I’m on my way!” she said.

Then she was off to Dulles Airport to catch a charter flight headed to Cedar Rapids, Iowa, for a busy schedule of campaign events.