Through the end of the third quarter, his campaign had spent $20.1 million of the $31.4 million it had raised since its inception, according to a New York Times analysis. Bush’s campaign, by contrast, had spent $14.5 million.

Watts, the communications director, siad that the large expenditures were a consequence of looking, successfully, for new donors. “It’s clearly an investment,” he said. “When you take the prospecting out of our program, our burn-rate is around 11 percent.”

Watts also insisted that the campaign is where it needs to be in terms of on-the-ground staffing. Others are not so sure. A New Hampshire Republican strategist who is not working for any presidential candidate told The Hill that Carson’s operation in the Granite State was “very small. He has one or two people but you don’t see any evidence of it.”

The conventional wisdom is that Carson’s stay at the top of the polls may not endure. But he has defied expectations many times before.

 “I would not bet on him today,” said Rollins, “but he has got a lot further than anybody thought he would go.”