“What the inspector general said last time was, the whistle-blower pulled the fire alarm,” Representative Mike Quigley, Democrat of Illinois, told reporters. “We have now seen the smoke and the fire.”

How the White House, which has routinely rejected congressional requests for information, responds to the demands for documents could significantly shape the impeachment investigation going forward. Under normal circumstances, the White House could claim materials referred to in both requests were privileged, using that as a defense in court.

Press secretaries for the White House and the vice president issued similar statements assailing the demands, but did not clearly indicate whether they would comply or not. Stephanie Grisham, the White House press secretary, said the subpoena “changes nothing” and called it “just more document requests, wasted time and taxpayer dollars that will ultimately show the president did nothing wrong.”

Katie Waldman, Mr. Pence’s press secretary, promptly said that “given the scope, it does not appear to be a serious request but just another attempt by the ‘Do Nothing Democrats’ to call attention to their partisan impeachment.”

But that will not help Mr. Trump’s case on Capitol Hill. Speaker Nancy Pelosi and the chairmen leading the inquiry have consistently warned the White House that noncompliance with their requests will be viewed as obstruction of Congress, itself a potentially impeachable offense.

“The White House has refused to engage with — or even respond to — multiple requests for documents from our Committees on a voluntary basis,” said the letter to Mr. Mulvaney, signed by Representative Adam B. Schiff of California, the Intelligence Committee chairman; Representative Eliot L. Engel of New York, the Foreign Affairs Committee chairman; and Representative Elijah E. Cummings of Maryland, the Oversight and Reform Committee chairman. “After nearly a month of stonewalling, it appears clear that the president has chosen the path of defiance, obstruction, and cover-up.”