Asked whether he expected Mr. Kudlow to return to work, Mr. Laffer said he had never considered the possibility that he would not.

“I don’t think there’s a chance he’ll resign,” Mr. Laffer said. “This is the culmination of his life. And it’s that time for Trump, too. He needs Larry.”

Mr. Laffer noted that Mr. Kudlow had pushed hard to be appointed to succeed the economic council’s previous director, Gary Cohn. “He really wants that job,” he said. “He really loves it.”

Mr. Kudlow had complained to colleagues of exhaustion in recent days. Friends said they had begun to worry about his health after he looked uncharacteristically fatigued at a series of events. He did not respond to messages from colleagues on Sunday and he canceled a key meeting on Monday, before being hospitalized and having doctors insert a stent.

Mr. Trump posted a message about Mr. Kudlow’s hospitalization on Twitter late Monday. A short time later, Ms. Sanders said in a statement that Mr. Kudlow was “currently in good condition at Walter Reed National Military Medical Center and his doctors expect he will make a full and speedy recovery.”

Mr. Kudlow is a former Wall Street economist and a frequent adviser on economic issues to conservative political candidates, including Mr. Trump, whose campaign tax plan Mr. Kudlow helped write. He was also a longtime radio and television host, including more than a decade on CNBC.

Mr. Laffer, whose friendship with Mr. Kudlow has spanned several decades, has spoken at least once a week with Mr. Kudlow since he started working at the White House. He said that Mr. Kudlow had occasionally complained about his health in the past, but had not done so since he began working for Mr. Trump.

“I do not think the stress levels at the White House are anything like he had at CNBC,” Mr. Laffer said.