Among Representative Melissa Hortman’s final votes in the Minnesota legislature was one she agonized over.

Lawmakers in the evenly split chamber had been in a bitter standoff over a Republican-backed provision that would make undocumented adults in Minnesota ineligible for the state’s health care program for low-income residents.

The fight, which could have led to a government shutdown, was resolved after Ms. Hortman, the top Democrat in the House, cast the lone Democratic vote in support of the measure earlier this month, paving the way for passage of the state budget.

“I know people will be hurt by that vote,” she told reporters afterward, breaking down in tears. “I did what leaders do. I stepped up and I got the job done for the people of Minnesota.”

The decision, colleagues said, was a prime example of the way Ms. Hortman thought about politics, often making a point of working across party lines and acting more as a pragmatist than an ideologue.

Colleagues remembered Ms. Hortman, who was fatally shot early Saturday in what officials described as a political assassination, as a hardworking, problem-solving leader who managed to negotiate her way through impasses, even within her own party, over two decades in the Legislature.