Top House Democrats are treading carefully on the issue of impeaching President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE, despite growing calls for action from the party's base and its crowded field of 2020 presidential candidates.

Amid shouts of “impeach” during comments at the California Democratic Party convention on Saturday, Speaker Nancy Pelosi Nancy PelosiHoyer: House should vote on COVID-19 aid — with or without a bipartisan deal Ruth Bader Ginsburg lies in repose at Supreme Court McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE stopped short of endorsing impeachment or signaling her intention to pursue it.

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The California Democrat instead spoke about what Trump could be “covering up” and accused him of “welcoming ... the assault on our democracy.”

She also vowed to continue various House investigations of Trump’s administration and businesses.

"This isn't about politics, it isn't about partisanship, Democrats versus Republicans, no," Pelosi said.

"It's about patriotism, it's about the sanctity of the Constitution and it's about the future of our nation," she added. "We will go where the facts lead us. We will insist on the truth. We will build an ironclad case to act."

Pelosi's stance has drawn the ire of the party’s progressive wing. That pressure has intensified since the release of special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE’s report and his rare public statement on the Russia investigation last week, when he said that if his team intended to say their findings exonerated Trump of criminal activity, “we would have said so.”

A top member of Pelosi's leadership team, House Majority Whip James Clyburn (D-S.C.), said Sunday, however, that he believes Trump will be impeached “at some point.”

Asked if he believes House Democrats will eventually begin impeachment proceedings, the third-ranking House Democrat told CNN’s Jake Tapper Jacob (Jake) Paul TapperThe media's misleading use of COVID-19 data Julia Louis-Dreyfus: 'We can't spend much time grieving' Ginsburg Pence aide dismisses concerns rushed vote on Trump nominee will hurt vulnerable senators MORE, "Yes, that's exactly what I feel."

Clyburn directly referenced Pelosi’s remarks one day earlier, telling Tapper, “What Nancy Pelosi is trying to do, and the rest of us in the House of Representatives, is to develop a process by which we can efficiently move on this issue so that when we get to a vote, it would be something that she calls ironclad, I call effective. And that is why we are trying to take our time and do this right.”

Clyburn also said that Democratic leadership is less concerned with the Republican-controlled Senate, where a two-thirds majority vote is needed to convict and remove a president from office, than with successfully convincing the public of the necessity of impeachment before the process can begin.

New polling indicates that while impeachment has risen in popularity since Mueller’s remarks, a majority remains opposed to it. A CNN poll released Sunday found that 41 percent of Americans support impeaching Trump, compared to 54 percent who oppose it. The percentage of Americans favoring impeachment is up 4 percentage points from last month, driven largely by increased support among Democrats, 76 percent of whom are now in favor.

But Republican Sen. John Kennedy John Neely KennedyMORE (R-La.) stressed on Sunday that a majority of Americans remain opposed to impeachment, saying the process “polls right up there with skim milk among the American people.”

Kennedy said that if Democrats have made up their minds to impeach Trump, continuing to debate about it was a waste of time.

"My advice to my Democratic friends is if you want to do it, go hard or go home," Kennedy said on CBS’s "Face the Nation."

"If you want to do it, go to Amazon online, buy a spine and do it. ... If you’re not going to do it, then let us get back to work," he added.

Calls for impeachment have grown increasingly common in the crowded Democratic presidential field as well.

Sen. Elizabeth Warren Elizabeth WarrenDimon: Wealth tax 'almost impossible to do' CNN's Don Lemon: 'Blow up the entire system' remark taken out of context Democrats shoot down talk of expanding Supreme Court MORE (D-Mass.) became the first candidate to call for it in April. Both Warren and Sen. Kamala Harris Kamala HarrisHarris faces pivotal moment with Supreme Court battle Nearly 40 Democratic senators call for climate change questions in debates Joe Biden has long forgotten North Carolina: Today's visit is too late MORE (D-Calif.) have said Mueller’s report and subsequent comments constituted an “impeachment referral.”

After Mueller’s public comments, Sens. Cory Booker Cory Anthony BookerBipartisan praise pours in after Ginsburg's death DHS opens probe into allegations at Georgia ICE facility Democratic lawmakers call for an investigation into allegations of medical neglect at Georgia ICE facility MORE (D-N.J.) and Kirsten Gillibrand Kirsten GillibrandSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Suburban moms are going to decide the 2020 election Jon Stewart urges Congress to help veterans exposed to burn pits MORE (D-N.Y.) also called for impeachment proceedings.

Sen. Michael Bennet Michael Farrand BennetOVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' Senate Democrats demand White House fire controversial head of public lands agency Next crisis, keep people working and give them raises MORE (D-Colo.), however, urged caution, saying last Thursday night that while he believes Trump has committed impeachable offenses, "we have to go through the process."

"One of the problems with our politics today is we want to go out and tweet and immediately react, a race to judgment, and we need to be more strategic than that," he added. "I'm not saying we shouldn't follow this evidence where it leads, but I am saying we should bring the American people."