Unlike Mr. Sanders, though, Mr. Carson has nothing against big money. This month he began a stretch of more than 30 fund-raising events from Bel Air in Los Angeles to South Carolina for donors willing to pay $500 to $2,700, the maximum gift to a candidate allowed by federal law.

The events were added to Mr. Carson’s schedule after he began surging in the polls, aides said. Earlier, big conservative donors had resisted Mr. Carson, said Doug Watts, a campaign spokesman. “They said, ‘Why don’t you prove your street cred first, and then we’ll be interested in making large donations,’ ” Mr. Watts said.

Having cleared that bar, Mr. Carson is hitting the private donor circuit in earnest. His goal: $5 million by the end of October.

Jennifer Hohman, a co-host of a fund-raising dinner for Mr. Carson in Houston next month, said she was soliciting affluent supporters of social programs for the homeless or for children in foster care, in hopes of raising $250,000. “This is Bush land,” she said, but added, “There are a lot of Republican establishment givers who aren’t wanting to support the establishment.”