“A lot of people feel defeated,” said Danny Villazon, 54, a lawyer. “Trump always wins. The Mueller report and then impeachment. It seems like nothing can stop him.”

Some Democratic officials and strategists argue that it’s far too early to panic, citing the quirky caucus process, which requires Iowans to spend hours on a cold winter evening publicly expressing their preferences.

Former Gov. Terry McAuliffe of Virginia said the lower-than-expected turnout in Iowa came as a surprise, after the kind of voting surges he’s seen in his home state. Last year, the highest number of voters in a generation for an “off-off year” election gave Democrats control of the House and Senate in Virginia for the first time in a generation.

“It’s hard one to figure because turnout everywhere else has been so high,” he said. “I’m going to lay it at the feet of this arcane caucus process. People just don’t have the time to do what needs to be done.”

Others cited the large number of undecided voters in Iowa, saying that as the race narrowed, larger numbers of Democrats would get engaged. In the run-up to the caucuses, polling showed that as many as 40 percent of voters said they had not made a final decision on a candidate. At primary events, voters frequently say they’d support any of the candidates over Mr. Trump, underscoring that their attention is far more focused on the president than on their own options for a nominee.

Tyler Jones, a South Carolina Democratic strategist who helped flip a Charleston district held by Republicans for nearly four decades, said he expected turnout to skyrocket once the contest moved to his state. By then, he predicts, the field will have narrowed to a clearer choice between Senator Bernie Sanders and a more moderate opponent.

“We are very top-heavy,” said Mr. Jones, who is unaffiliated in the race. “We have very similar candidates, and you have to be deliberatively picky.”