Mr. Rubio’s supporters say they believe a credible sum to have in his campaign bank account when candidates report their totals would be in the neighborhood of $10 million. His super PAC, they said, should have roughly twice that.

But not all has been going as smoothly as hoped. The campaign canceled two fund-raisers last month in Florida because not enough donors committed. A top Washington-based fund-raiser for Mr. Rubio, Carmen Miller Spence, just resigned her position with the campaign. A Rubio spokesman declined to comment on Ms. Spence’s exit but said the canceled events would be rescheduled.

“All my friends — all my friends — it seems everybody over 70 is for Jeb Bush,” said Gay Gaines, a Rubio supporter who has held fund-raisers for him at her Palm Beach home. “It’s not that I don’t think Jeb is fabulous — I do. But I said to all of them: ‘You know what worries me? The millennials. They’re not going to want another Bush.’”

“It kills me,” she added.