Facing a relatively safe re-election race, Ms. Klobuchar spent most of the midterms promoting other Democrats running for office in her home state. She has made numerous visits to Iowa during her 12 years in office, most recently to push a message of “heartland economics” to rural residents and farmers, arguing that Democrats cannot afford to forget about the middle of the country.

“Minnesota matters, Wisconsin matters, Nebraska matters, Ohio matters — and, yes, Iowa matters,” she told the Iowa Farmers Union in December.

Ms. Klobuchar believes the contiguous location of her home state to Iowa could give her an advantage in the state’s caucuses, a crucial first test of the primary field. On Sunday, she quipped that the state is where Minnesotans “go south for the winter.”

Ms. Klobuchar grew up in the Minneapolis suburbs as the daughter of a schoolteacher and a columnist for The Minneapolis Star Tribune. After graduating from Yale and the University of Chicago Law School, she returned to Minnesota to work as a corporate lawyer. The birth of her daughter, who was born with a condition that required her to remain in the hospital, plunged her into political activism. Ms. Klobuchar pushed for legislation that would guarantee new mothers a 48-hour hospital stay, a proposal that eventually became federal law. She was elected prosecutor for the state’s most populous county in 1998 and became the first elected female senator from her state in 2006.

In the Senate, Ms. Klobuchar has cultivated a worker-bee persona, not leading on divisive issues like immigration and focusing instead on curbing the cost of prescription drugs, addressing sexual harassment and protecting online privacy. A 2016 analysis found that she had passed the most laws of anyone in the Senate.

Ms. Klobuchar rose to national prominence during the Senate Judiciary Committee hearing for Justice Brett M. Kavanaugh, when she pressed the nominee on whether he had blacked out drinking. “Have you?” he shot back, to which she calmly replied, “I have no drinking problem, Judge.”

“When I turned on the TV and watched that hearing, I was so damn proud she was our senator,” said Gov. Tim Walz, one of several Minnesota officials who spoke at Ms. Klobuchar’s event.