“I took that as a signal that he’s not concerned about the upper 1 percent or 5 percent, he’s concerned about hopefully middle-class Americans,” he said. “Proof’s in the pudding. We’ll see how it comes out.”

That gathering was one of a series of bipartisan efforts to push the tax overhaul. He held a dinner Tuesday night with senators from both parties where tax matters dominated the conversation. On Wednesday night, the president was set to dine with Congress’s top Democrats, Senator Chuck Schumer of New York and Representative Nancy Pelosi of California.

To old hands of America’s biggest tax policy battles, the Republicans’ accelerated timeline appears virtually impossible. One big reason: the diminished standing of Gary D. Cohn, director of the president’s National Economic Council, and Steven Mnuchin, his Treasury secretary. That diminution is largely of the team’s own making; Mr. Trump has let it be known that Mr. Cohn is in disfavor for publicly disparaging the president’s response to violent racists in Charlottesville, Va., and Mr. Mnuchin suffered public scorn after jetting to Kentucky on a government plane with his wife to witness the solar eclipse.

Their stature stands in contrast to the experienced players who shepherded the last major tax overhaul in 1986.

“Things are quite anarchic across the board right now, and that’s not helping at all,” said C. Eugene Steuerle, who served as the coordinator of the Treasury Department’s tax reform effort from 1984 to 1986.

Last week, Mr. Trump blindsided Mr. Mnuchin during negotiations over lifting the government’s statutory borrowing limit — an issue that is central to the job of Treasury secretary. Mr. Mnuchin was pushing for an 18-month extension of the debt limit before Mr. Trump interrupted him and sided with Mr. Schumer and Ms. Pelosi, who wanted a three-month extension.

The White House press secretary, Sarah Huckabee Sanders, insisted this week that Mr. Trump had “confidence” in Mr. Mnuchin, but the rift over the debt limit left many observers wondering if his public stances on taxes could still be trusted.