Ahead of the meeting Friday, at least half a dozen top donors to Ms. Harris’s campaign told The Wall Street Journal that they were looking for her to pick up momentum heading into the fall, when more voters traditionally tune in to the primary.

But some also said they feared the Democratic primary is increasingly becoming a three-way race between Mr. Biden, Sen. Elizabeth Warren of Massachusetts and Sen. Bernie Sanders of Vermont.

Some of the donors said they—and others they had talked to—could shift some of their support to Mr. Biden if Ms. Harris’s poll numbers didn’t start trending upward…

Ms. Harris’s donors and those close to her campaign said they have been surprised by the resiliency of Mr. Biden’s support, especially among African-American voters in South Carolina, which they had seen as a state she could carry, but which has struggled to get a footing in.