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(CNN) —  

House Speaker Nancy Pelosi is facing pressure from within her own leadership ranks to take a more aggressive strategy toward impeachment even as Pelosi made clear that she is pursuing a deliberate approach.

House Judiciary Chairman Jerry Nadler discussed with Pelosi the advantages of an impeachment inquiry in terms of adding weight to a court case, according to a source with direct knowledge. Nadler, whose committee has been on the front lines of investigating the findings from within special counsel Robert Mueller’s report, broached the topic with Pelosi because several members of his committee have been pressing to open an inquiry.

The House Democrats’ debate took place behind closed doors in several meetings Monday evening – in Pelosi’s leadership office, in a larger meeting of the Democratic steering committee and in the House Judiciary Committee.

Pelosi made clear to Nadler that Democratic-led investigations won a key court case earlier Monday and their approach is getting results, according to the source. Pelosi made a similar case at the larger Democratic meeting and Nadler agreed with that approach when they met.

The tensions displayed behind closed doors underscore the growing divide within the caucus about how to proceed in the face of White House resistance to all its demands, as Pelosi and some of her top confidants argue that acting with too much haste would be a gift to their political foes while a growing faction of Democrats – that now includes several high-profile and high-ranking members – push them to take a tougher stand against what they call a lawless President.

House Intelligence Chairman Adam Schiff, who has been skeptical of impeachment, told CNN on Tuesday morning that the “case gets stronger the more they stonewall.”

House Budget Chairman John Yarmuth said Tuesday morning that waiting until the fall would be “too late” to begin an impeachment inquiry, telling CNN, “I think it’s time” to begin the proceedings.

Rep. David Cicilline, a member of the Democratic leadership team and the House Judiciary Committee, was among those Democrats who argued during a closed-door meeting Monday night with Pelosi that the panel should begin an impeachment inquiry to hold the President accountable for the stonewalling.

Rep. Steve Cohen, who also sits on the committee, asked Pelosi why she doesn’t support impeachment. Pelosi for her part defended their approach, saying that one thing will lead to another and argued that the committees are on a course of action to be successful.

The renewed divisions came as the administration has continued to rebuff congressional demands for documents and testimony, including from former White House counsel Don McGahn, who the White House has directed not to testify before the House Judiciary Committee on Tuesday.

In public, Nadler has been resistant to launching impeachment proceedings but has left the door open.

“There’s a lot of considerations on that,” Nadler said Monday on CNN’s “Cuomo Prime Time.” “We may do that.”

At a meeting with House Democrats on the steering committee Monday night, Cohen asked Pelosi why she did not support impeachment. According to three Democratic sources, Pelosi went around the room and let members voice their opinions on the matter, then laid down her own view.

Pelosi said the committees were on course to be successful and Democrats’ message must be “No one is above the law,” and that they are witnessing “the cover-up.”

The California Democrat also said they all agreed they needed to get to the truth, but that the public believes kitchen table issues must also be dealt with.

Speaking to reporters Monday about their views on impeachment, Cicilline and Rep. Hakeem Jeffries of New York – both members of Democratic leadership and the House Judiciary Committee – expressed opposite opinions about how to proceed amid White House resistance to their demands.

Cicilline said he would argue that the “time has come” for an impeachment inquiry if McGahn does not show up before the judiciary panel on Tuesday.

“We have a responsibility at some point to open up an inquiry if this kind of obstruction and interference and stonewalling of the entire investigation continues,” Cicilline said.

Jeffries was somewhat optimistic, asking why Democrats should move to open an impeachment inquiry if they were winning in the court system. He said they would have a “discussion about the best way to proceed” and had “laid out a methodical approach.”

“That approach, I think, was validated today by the decision that was made in the Mazars case, showing that Congress does have constitutionally anchored oversight responsibility to ask questions and obtain documentation, notwithstanding the fact that we see the stonewaller in chief and his flunkies in the executive branch suggesting otherwise,” Jeffries said.

Asked further about opening an impeachment inquiry at this point, Jeffries responded, “The question is why would we open an impeachment inquiry If we’re winning?”

But other rank-and-file members are making their feelings on impeachment well known. A member of House Judiciary, Rep. Veronica Escobar of Texas, said she’s concerned with the leadership’s hesitance and called for immediate action on impeachment.

And Rep. Joaquin Castro, a member of the House Intelligence Committee, told CNN that it’s time to begin immediately given the White House stonewalling.

This story has been updated with additional developments Tuesday.