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.