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Unlike in 2016, when the Democratic donor class rallied to Hillary Clinton, or 2008, when givers lined up with Mrs. Clinton, Barack Obama and John Edwards, many of the party’s wealthiest figures remain firmly on the sidelines, serving as perhaps the biggest check on the role of big money in 2020 to date.

That has given an advantage to Mr. O’Rourke and Mr. Sanders, who are banking on small donations. Those two, plus Ms. Harris, who has a strong small-donor network and has been aggressively courting larger contributors, are widely expected to raise the most in the first quarter.

Several 2020 hopefuls have spent recent weeks canvassing the country, from Dallas to Miami, Chicago to Los Angeles, to raise the money needed in a crowded primary that is expected to easily cost hundreds of millions of dollars.

At fund-raising events, attendees say, most 2020 candidates typically are delivering more intimate versions of their stump speeches, pitching their vision for the country along with a heavy dosage on their political viability and pathway to the presidency, amid caterers circulating with drinks and snacks.

Last Tuesday, Ms. Harris was in the tony Washington neighborhood of Kalorama at an event where hosts were asked to raise at least $10,000 (although the price points were not listed on the front of at least one version of the emailed invitation). The Saturday before that, Mr. Booker was feted at the home of Gov. Phil Murphy of New Jersey as the singer Jon Bon Jovi circulated in the crowd ahead of a three-course dinner that pulled in $300,000, according to a person familiar with the event. And before that, Senator Amy Klobuchar was in Chicago asking for money at the home of a former Goldman Sachs banker who later served as ambassador to Canada, Bruce A. Heyman.

In between, donors are hearing from the candidates by phone. A lot.

“When I see a 202 number these days, I don’t usually answer it,” said Amber Mostyn, a Houston-based attorney and prominent Democratic fund-raiser, joking about the Washington area code and the number of candidates who have reached out for help.