WASHINGTON — The debate over whether to open an impeachment inquiry against President Donald Trump intensified among House Democrats on Tuesday as former White House counsel Don McGahn defied a congressional subpoena to provide testimony.

“There’s a growing understanding that the impeachment process is inevitable — when, not if,” House Budget Committee Chairman John Yarmuth, D-Ky., said to reporters as he entered a closed-door House Democratic Caucus meeting in the basement of the Capitol.

Rep. Alexandria Ocasio-Cortez, D-N.Y., who has signed onto a resolution that calls for the House Judiciary Committee, to look into whether to launch impeachment proceedings, told NBC News’ Kasie Hunt on Tuesday, “I believe we have come to a time of impeachment."

Asked at what point she thought Pelosi would agree, Ocasio-Cortez said public pressure would be the deciding factor. “I think it really depends on everyday Americans," she said. "If you have a representative that is in a close seat and you think that we should be upholding the rule of law, I think it's time to give your representative a call.”

Rep. Diana DeGette, D-Colo., a 12-term lawmaker, announced on Twitter Tuesday that she backs the initiation of an impeachment inquiry.

The facts laid out in the Mueller report, coupled with this administration’s ongoing attempts to stonewall Congress, leave us no other choice: It is time for Congress to officially launch an impeachment inquiry against the President of the United States. — Rep. Diana DeGette (@RepDianaDeGette) May 21, 2019

Calls for impeachment proceedings by some members of Democratic leadership have grown this week as the White House continues to block Democrats from testimony or documents they’ve subpoenaed.

Download the NBC News app for breaking news and politics

Several Democrats on the Judiciary Committee pressed House Speaker Nancy Pelosi, D-Calif., Monday evening during a leadership meeting on Capitol Hill to move forward with an impeachment inquiry against Trump if McGahn failed to appear at the planned hearing, reviving a debate that has divided the caucus.

“I’m not there yet, but a couple more moves like the latest [with McGahn now showing up] is probably going to push me over the edge,” Rep. Emanuel Cleaver, D-Mo., told reporters after the closed-door meeting Tuesday morning.

“Every time someone refuses to testify, every time the president blocks another civilian ... from testifying, he is putting his thumb in our faces and the Constitution, frankly. I think more and more people are saying, ‘You know, he’s pushing us to the edge,’” he added.

As some Democratic members call for more forceful action, Pelosi has scheduled a special closed-door caucus meeting for Wednesday morning to give an update on oversight and investigations, two Democratic leadership aides told NBC News on Tuesday.

Rep. Jan Schakowsky, D-Ill., told reporters Tuesday that she expects the Wednesday meeting will focus on growing calls for impeachment.

“I think we’re going to have an important meeting tomorrow to discuss [it],” said Schakowsky, who described the caucus as “somewhat divided” over the issue and is unsure about an impeachment inquiry herself. “I believe that he has definitely committed impeachable offenses — the question is how do we follow up on all of the misdeeds that we’ve seen?”

Three members of the Judiciary Committee and leadership — Reps. Jamie Raskin of Maryland, David Cicilline of Rhode Island and Joe Neguse of Colorado — lobbied Pelosi Monday to initiate impeachment proceedings.

“I do think this effort by the president and the White House to impede and undermine our ability to collect the evidence necessary to do our work is something that can’t be tolerated,” Cicilline told reporters Tuesday after the caucus meeting.

The decision about whether to pursue impeachment “will be a collective decision” among House Democratic leaders, Cicilline said, that will be reflected by the sentiment of the entire caucus and “ultimately decided by the speaker.”

House Majority Leader Steny Hoyer, D-Md., continued to echo Pelosi's cautious tone on impeachment. "I don't think we're there at this point in time," he told reporters Tuesday.

Many of the Democrats pushing to maintain the current trajectory argued that a ruling by a federal judge Monday in favor of the House Oversight Committee's bid to obtain Trump's financial records from his accounting firm meant impeachment was not needed to continue investigations.

“I think we need to make sure that we do as much investigating as we can. And if that leads us to looking into impeachment, we’ll get there. But one step at a time,” said Rep. Debbie Wasserman Schultz, D-Fla., who served as chairwoman of the Democratic National Committee, during the period when the Russians hacked into the committee.

“The court ruling yesterday was pretty telling in that we don't need impeachment at all to be able to move forward with the investigations, and so I think that right now we have the legal, you know, legal aspects on our side, and we need to continue forward on that path,” said freshman Rep. Katie Hill, D-Calif., Tuesday.

“We don’t need impeachment,” Rep. Bill Pascrell, D-N.J., added Tuesday. “I say, invoke the penalties. Put them in contempt. You’ve got to put the heat on these boys. They don’t know anything but heat, we have the law on our side, we should apply the heat.”

But some impeachment advocates sounded emboldened. "I am convinced that there will be a vote on impeachment, and I am convinced that people are starting to conclude that it should be sooner rather than later,” Rep. Al Green, D-Texas, who has previously introduced articles of impeachment against Trump, told reporters Tuesday.

Earlier Tuesday, House Judiciary Chairman Jerrold Nadler, D-N.Y., held the planned hearing for McGahn with an empty witness chair.

"This conduct is not remotely acceptable," the New York Democrat said then. "Mr. McGahn did not appear today because the president prevented it ... "

"Our subpoenas are not optional," Nadler continued. "Mr. McGahn has a legal obligation to be here for this scheduled appearance. If he does not immediately correct his mistake, this committee will have no choice but to enforce the subpoena against him."

Rep. Doug Collins, R-Ga., the committee's ranking member, called the empty chair hearing "theater" and said calling McGahn to testify was not about obtaining information or informing legislation, but "embarrassing and harassing the president."

"Democrats are trying to make something out of nothing," Collins said.

An attorney for McGahn, William Burck, had confirmed in a letter to Nadler Monday that his client would not appear for his scheduled hearing, citing both the Justice Department's legal opinion that McGahn cannot be compelled by subpoena to testify and Trump's "unambiguously" clear directive that McGahn defy Congress.