“There are all these streams and creeks of offenses that seem to be converging into a bigger river — impeachment,” said Representative Jamie Raskin, a Maryland Democrat and former constitutional law professor who serves on the Judiciary Committee.

“There is nothing to explain how the executive branch can defy, categorically, every lawful request for information from the Congress of the United States,” added Mr. Raskin, who said he is open to the idea of a limited impeachment inquiry. “President Trump’s defiance of Congress is far more comprehensive and sweeping than anything Congress experienced during the Watergate period.”

Several Democrats close to Ms. Pelosi said that impeachment still remained unlikely, cautioning that Mr. Trump’s threats alone were not enough to spur such action. And her leadership team is keenly aware that Mr. Trump “is goading us” into making a political mistake, according to Representative Hakeem Jeffries, Democrat of New York, who is chairman of the House Democratic Caucus.

Ms. Pelosi cautioned Democrats against getting too carried away with impeachment talk.

“While we may have our difficulties in other areas, we cannot, we cannot, we cannot ignore the needs of the American people as we go forward,” Ms. Pelosi said after meeting with the president about kick-starting a long-dormant infrastructure funding bill.

But sentiment appears to have shifted significantly over the past week.

“I am not there yet, but I have to say that the president’s obstruction of Congress now following his obstruction of the Justice Department is certainly adding new heft to the idea that he has to be held accountable,” Representative Adam B. Schiff of California, chairman of the Intelligence Committee, said in an interview.