Washington (CNN) House Democrats who are publicly and privately agitating to begin impeachment proceedings against President Donald Trump are growing worried that their time is running short -- and that they are missing key opportunities to give them a clear opening to mount a formal probe.

New York Rep. Jerry Nadler, the chairman of the House Judiciary Committee who would be in charge of leading an impeachment inquiry, has repeatedly made a behind-the-scenes case to House Speaker Nancy Pelosi and others to begin a probe, according to multiple people familiar with the matter.

Nadler has told his colleagues that there are moments with the country paying close attention that would give them a clear opportunity to formally open up an inquiry, according to people who have spoken to him, with Democrats pointing to the immediate aftermath of former special counsel Robert Mueller's report and this week's public testimony as those key times.

While those moments could still occur as Democrats mount court battles to unearth more information from Trump and the White House, a number of other Democrats are fretting those chances now may never materialize with the House beginning a six-week summer recess, a dwindling number of legislative days left this year and the 2020 campaign season around the corner.

After the Mueller hearing, Nadler floated at a closed-door caucus meeting the option of drafting articles of impeachment, along with five other committees that are leading investigations into the President, according to multiple sources. He also indicated his panel could move forward on impeachment proceedings without a full vote of the House, according to attendees.

On Thursday, two Democratic chairmen who are also investigating Trump, Reps. Adam Schiff of California and Elijah Cummings of Maryland, told CNN they could support formal impeachment proceedings if Trump were to defy a court order, but they stopped short of backing an inquiry now.

Pelosi allies see change in tone

Still, several Democrats who are close to Pelosi believe her tone has shifted over opening an impeachment probe. After listening to her members at the closed-door caucus meeting, Pelosi indicated that the House Democrats need to have their strongest possible case to move forward on impeachment and that they would fight the White House in the courts first, signaling that any decision would not be made by any individual person but the full caucus instead, according to sources who attended the meeting.

And after weeks of throwing cold water on moving forward because Republicans in the Senate would kill such an effort, Pelosi indicated Wednesday evening that resistance in the Senate is no longer a chief concern of hers, arguing instead they plan to focus their efforts in court to get information while noting that "this isn't endless."

"The stronger our case is the worse the Senate will look for just letting the President off the hook," Pelosi told reporters.

Several Pelosi allies told CNN they interpreted her remarks as a clear shift and an indication she's keeping open the option of supporting impeachment proceedings, even though she has yet to embrace going down that route.

"I think she's slowly coming around to it," one Democratic lawmaker said privately, asking for confidentiality to discuss his interactions with the speaker.

Yet some Democrats believe that their party is moving too slowly and will miss their opportunity, especially given the lack of legislative days before 2020, when the campaign season will make lawmakers more risk-averse.

"This is all an agenda that has to happen in 2019 if it's going to happen," said Rep. Jamie Raskin, a member of the House Judiciary Committee and advocate of an impeachment inquiry. "So the clock is ticking."

"Time is slipping away," said Rep. Al Green, a Texas Democrat and vocal proponent of impeachment . "And we do have to make some decisions about impeachment in the not too distant future."

Others are growing increasingly frustrated at what they view as a too timid response to investigate Trump and fight him in court.

"I would certainly like to see us move more expeditiously," said Rep. Lloyd Doggett, a member of the Ways and Means Committee, whose lawsuit for Trump's tax returns wasn't initiated until this month. "And so we're waiting on the results of litigation so we could be waiting indefinitely."

Asked about Pelosi's approach, Doggett told CNN: "Well, I want to encourage her to expedite this matter more than it has been in the past."

Rep. John Garamendi, Pelosi's fellow California Democrat, had a more ominous warning Thursday for his party if the House doesn't move forward with impeachment proceedings.

"The risk is that we have abandoned our responsibility," Garamendi said. "The risk is ours. It's really the future of our constitutional division of power."

Searching for an impeachment spark

What remains to be seen is what ultimately would be the triggering event to spark an impeachment probe.

Already, some Democrats believe that they missed opportunities to trigger an impeachment probe in the immediate aftermath of the Mueller report , and that his Wednesday hearing, after the former special counsel laid out instances where Trump allegedly obstructed justice, didn't exonerate Trump and made clear he was bound by Justice Department policies prohibiting the indictment of a sitting President.

After Mueller's shaky testimony , fewer Democrats have come out to publicly call for an impeachment inquiry than some in their party had initially believed. Only a few Democrats have so far signed onto an impeachment inquiry in the wake of Mueller's testimony, far short of any groundswell.

"Well, I don't think it had as big of an impact that many had thought," said Rep. Harley Rouda, a freshman from California who supports an impeachment probe. "We should not be focused on the performance of Mueller in these hearings . We should be focused on the facts that were presented. And the facts that were presented are damning."

The next step for Democrats is to push for more information in the courts, which Pelosi said had to play out before a decision could be made on impeachment. Nadler said Wednesday that the House would soon be filing lawsuits to obtain Mueller's grand jury information from the courts and to force former White House counsel Don McGahn to comply with the committee's subpoena.

Some powerful Democratic chairmen are still reluctant about launching an impeachment probe but argue that should Trump defy court orders, they would likely support formal proceedings.

"There are a number of things that may push me over the edge," Schiff, the House Intelligence Committee chairman, said Thursday. "Certainly when we get to the point in litigation where the Trump Administration can no longer appeal, should they refuse to abide by a lawful court order, we may really be in a constitutional crisis. And that would be enough for me."

Schiff added: "But I may get there before that. The administration is doing everything it can to move us in that direction."

Cummings, the House Oversight chairman, made a similar case in an interview with CNN on Thursday.

"If he begins to disobey court orders, I think that I would really take a look at," Cummings said of an impeachment probe.