On Monday night, friends and colleagues expressed concern for his health. Kevin Hassett, the chairman of the White House Council of Economic Advisers, praised Mr. Kudlow in a brief interview. “Larry Kudlow is the salt of the earth, and a true patriot,” Mr. Hassett said. “And our thoughts and prayers are with him and his family tonight.”

Stephen Moore, a Heritage Foundation economist and longtime friend of Mr. Kudlow’s, said in an email Monday night that “he’s ok and will be back on the job,” in response to a question about Mr. Kudlow’s condition.

Mr. Kudlow is a smoker, and was sometimes seen outside the West Wing with a cigarette. He has told people the stress of the director’s job has surprised him, in part because of the constant level of toxic infighting among White House advisers, which he was not expecting.

Mr. Kudlow dove into the job with gusto, taking on a wide portfolio that included the president’s roller-coaster trade agenda — including on-again-off-again tariff threats against China, Mexico, Canada, the European Union and others — and denuclearization negotiations with North Korea. But in recent days, he has complained of exhaustion to friends and reporters, while stressing how much he loved the job.

A disciple of the supply-side economic theories of the economist Arthur Laffer, Mr. Kudlow struggled with drug and alcohol addiction in the early 1990s while chief economist at the Wall Street firm Bear Stearns. He found sobriety, in part through Catholicism, and then he found a comfortable niche as a television commentator, radio host and evangelist for the economic power of low taxes, light regulation and a strong dollar.

He was an early fan of Mr. Trump’s presidential campaign, and he helped shape its tax plan, along with Mr. Moore. After Mr. Trump’s election, Mr. Kudlow was a loud and frequent champion of the tax cuts that Mr. Trump signed into law in December.

“He’s an optimist, he’s a markets guy, he always says profits are the mother’s milk,” James Pethokoukis, a columnist for the conservative American Enterprise Institute, said when Mr. Kudlow was picked for the National Economic Council job. When markets are firing and growth is strong, he said, “that is energizing to him.”