“President Trump cannot permit his administration to participate in this partisan inquiry under these circumstances,” wrote Pat Cipollone, the White House counsel.

And yet the president has been unable to prevent it.

Just since Mr. Trump declared war on the impeachment effort, three current and former senior State Department officials and a former top White House aide have testified for nearly 36 total hours, delivering to lawmakers a consistent narrative of how they were effectively pushed aside by allies of the president operating outside America’s usual foreign policy channels.

“It’s partly because this shadow foreign policy that the president was running was so deeply offensive to people in his own administration who took pride in overseeing a professionally run and arguably exemplary policy in support of Ukraine,” said Representative Tom Malinowski, Democrat of New Jersey and a former State Department official involved in the inquiry. Referring to Mr. Trump’s personal lawyer, he added, “And then to see the official policy undermined by this clownishly corrupt effort led by Rudy Giuliani on behalf of the president was just more than many people apparently could bear.”

Republicans who control the Senate view the fast-building case as serious enough to begin preparing for the trial in their chamber that would follow impeachment by the House. Senator Mitch McConnell, Republican of Kentucky and the majority leader, briefed fellow lawmakers over lunch on Wednesday about how a trial would work, expressing his hope of conducting it speedily and completing it by the end of the year, people familiar with his remarks said.

Facing accusations of secrecy from Republicans, Representative Adam B. Schiff, Democrat of California and the chairman of the Intelligence Committee, informed colleagues on Wednesday that he planned to open the inquiry to the public soon. He wrote that he planned to release transcripts of all the interviews as the investigation proceeded and pledged to soon hold public hearings “so that the full Congress and the American people can hear their testimony firsthand.”

For Mr. Trump, who is famous for demanding fierce loyalty from those around him, the daily — or even hourly — crush of damaging headlines is an infuriating departure from previous successes in controlling disclosures to Congress from people in his orbit.

During the congressional investigation into Russia’s election meddling, Mr. Trump blocked a deposition of Donald F. McGahn II, his former White House counsel, and dramatically limited testimony from some of his closest aides, including Hope Hicks, the former White House communications director, and Corey Lewandowski, his former campaign manager.