In the Senate, Ms. Klobuchar is not in the forefront on divisive issues like immigration, but she has led efforts to curb the skyrocketing cost of prescription drugs, expand voting rights, address sexual harassment and protect online privacy after revelations of Facebook’s data mining.

Early in her tenure, she carved out a niche in consumer protection, shepherding passage of bipartisan bills to ban lead in toys and improve swimming pool safety after several highly publicized child deaths, measures that Gregg Peppin, a Republican strategist here, said have earned Ms. Klobuchar a derisive nickname: “The Senator of Small Things.”

“It’s issues that are kind of no-brainers, and when it comes to substantive things, she’s really not there,” Mr. Peppin said, adding that Republicans have a second nickname for her: “Cotton Candy Amy, because there’s no nutritional value; you put it in your mouth and it melts away and there’s nothing really there.”

Ms. Klobuchar has heard the “small things” criticism, and resents it.

“Not for a minute do I view these as small things,” she said sharply. “They’re big things for the people whose kids’ lives were saved.”

On Capitol Hill, Ms. Klobuchar’s reputation is not all sweetness and light; she is said to be brutal to work for. A survey of senators by the website LegiStorm found that from 2001 to 2016, her office had the highest turnover, which earned her a prominent mention in a Politico article headlined “The ‘Worst Bosses’ in Congress?” (By 2017, two colleagues — John Kennedy of Louisiana and Chris Van Hollen of Maryland — had surpassed her.)

She acknowledged that she is demanding: “I have high expectations.”

But outwardly, Ms. Klobuchar is the embodiment of “Minnesota nice” — polite and intent on being able to “disagree without being disagreeable,” as she wrote in her 2015 memoir, “The Senator Next Door.” In an era of Twitter rants and senatorial showboats, she is the worker bee in the background, tallying up how many of her bills get signed into law: 24, she said, since Mr. Trump became president.