MASON CITY, Iowa — Before last week, Beth Kundel Vogel was undecided when it came to the Democratic presidential hopefuls.

But in the debate on Tuesday, Senator Amy Klobuchar of Minnesota impressed her by calling out Senator Elizabeth Warren of Massachusetts for offering voters a “pipe dream” rather than a plan to pay for universal health care.

And on Friday, Ms. Kundel Vogel heard Ms. Klobuchar speak passionately in Davenport, Iowa, about one way of thinking about the 2020 race: the need to win support beyond the party base. “We have to remember that nearly 10 percent of Trump voters voted for Barack Obama,” Ms. Klobuchar said. “It’s our job to bring them in.”

“Seeing her in person just closed the deal for me,” said Ms. Kundel Vogel, 47, a human resources manager. “She understands what it’s going to take to win, which is to win over independents and former Trump voters.”