NEWTON, Iowa — Lois Grier knows she has to make a decision about the Democratic primary soon.

She and her husband, Ted, traveled from their home in Otley to hear Bernie Sanders on Saturday and hoped to see Pete Buttigieg, too. But though Ms. Grier, 62, cares about issues like health care, what she is yearning to find above all is a White House hopeful she believes can defeat President Trump.

She hasn’t found one yet.

“It’s important to narrow it in to somebody that can beat Trump,” she said, adding that she would be watching the debate on Tuesday in Des Moines closely for telltale signs.

“A lot of the candidates are saying the right things,” she added. “But are they strong enough?”

For a year now, Iowans have been analyzing Democratic candidates for president, weighing their policies and personalities with the knowledge that the choices they make on caucus night on Feb. 3 could determine the trajectory of the primary. But with the first-in-the-nation caucuses three weeks away, many people in the state are still trying to make their decisions: A Des Moines Register poll last week showed that only 40 percent of likely Democratic caucusgoers had made up their minds. Nearly half said they could be persuaded to support another candidate as their top choice, and 13 percent said they did not have a first choice.

This level of uncertainty, verging on anxiety and even panic for some caucusgoers, reflects the stakes for Democrats as they seek a nominee who can do effective battle with Mr. Trump. Many Iowans worry that none of the top contenders have clearly proved themselves able to defeat the president.