Over the next three to five years, Mr. Carson hopes to establish more than 3,000 of the centers to provide low-income families, especially young people, with one-stop access to educational, job training, mentorship and health care services. But Ms. Greenwood argued that Mr. Carson’s team was not experienced enough to make it work, and it soon became apparent that there was little appetite in the White House for more than a pittance in funding — $2 million over the next year.

In response, Mr. Carson has turned to charitable foundations for funding. But he has not proved to be the best pitchman, according to a dozen attendees at a January meeting with potential donors at HUD headquarters. He began with a libertarian lecture, extolling the genius of the 19th-century robber barons who created the country’s philanthropic charities. They had spared the country from “European socialism,” he said.

One skeptical foundation officer countered by asking the secretary where “the public” part of the public-private partnership was coming from. Another asked, “What does this have to do with public housing?”

But his audience, mainly composed of community development specialists who believe that the government has an enduring moral responsibility to help the poor, was most put off by Mr. Carson’s assertion that the goal of EnVision was to put HUD out of business.

“There is nothing wrong with encouraging safe, inviting places for youth to grow,” said Adrianne Todman, chief executive of the Washington-based National Association of Housing and Redevelopment Officials. “But it is time for us to focus on the ‘H’ in HUD — ‘housing.’”