Senate Democrats are putting the brakes on impeachment chatter in the House, cautioning that lawmakers need to do more work before even thinking about moving forward on the issue.

A number of steps should be taken before there can be a serious discussion about 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, including hearing testimony from 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, say several Senate Democrats.

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They also want the House to review the unredacted version of his report and its underlying documentation.

“We ought to get the full report unredacted, get the underlying documentation, have Mueller come testify, and then we can make decisions on where to go,” Senate Minority Leader Charles Schumer Chuck SchumerCruz blocks amended resolution honoring Ginsburg over language about her dying wish Senate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' MORE (D-N.Y.) said Tuesday.

“We need to see the whole truth. Then we’ll make decisions on impeachment,” he added.

Sens. 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.) and 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.), who are both running for president, have come out in favor of starting impeachment proceedings, but they’re alone among Senate Democrats so far.

Even Sen. Richard Blumenthal (D-Conn.), one of Trump’s most outspoken critics, conceded Wednesday that “we need to present the case to the American people.”

“We need to present the evidence here before a decision is made on whether impeachment is pursued,” he said. “Very few Americans are going to read the Mueller report.”

Senate Democrats say there’s not enough public support to push ahead with impeachment without the danger of it backfiring — just as they say it did for Republicans in 1998 when they impeached then-President Clinton.

One senior Democrat, who requested anonymity to speak freely about the impeachment calls, noted that Democrats picked up seats in the House after Republicans impeached Clinton.

The lawmaker added that it would be close to impossible to muster the 20 Republican votes needed to reach 67 votes to convict Trump in the Senate on any House-passed articles of impeachment — an argument that has also repeatedly been underlined by 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 (D-Calif.), who has sounded a cautious note on impeachment.

Sen. Dianne Feinstein Dianne Emiel FeinsteinFeinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Democrats shoot down talk of expanding Supreme Court Biden leads Trump by 12 points among Catholic voters: poll MORE (Calif.), the ranking Democrat on the Senate Judiciary Committee, noted that Democrats on her panel have asked for Mueller to appear before them. She said this would be an important test of the Trump administration.

“The Mueller report — I read a lot of reports, I really do — it was a tough read to read every line of those two volumes,” she said. “I think we need to finish collecting and looking at that report. And I think it’s vital that Mueller come before [us.]”

Democrats in tough reelection races next year are trying to tamp down talk of impeachment, which would rev up the conservative base and likely turn off swing voters.

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Sen. Doug Jones (D-Ala.) says that while some of the president’s conduct as described in the Mueller report was “borderline appalling,” he does not favor impeachment.

“I’m not for that,” he said. “There needs to be some oversight, and we’ll see how that goes.”

He says the focus should be on strengthening U.S. voting systems and safeguarding future elections instead of on Trump’s “personal issues.”

Senate Democratic Whip Dick Durbin Richard (Dick) Joseph DurbinFeinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Grand jury charges no officers in Breonna Taylor death Democrats shoot down talk of expanding Supreme Court MORE (Ill.) on Monday said it’s “too early” to begin impeachment proceedings and urged House lawmakers instead to “gather information, evidence, testimony.”

Sen. 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.), who is also running for president, has broken with Warren and Harris by joining other Democratic lawmakers who say there needs to be more investigation before floating the prospect of impeachment.

“I think right now we should continue this investigation. I think Mueller should come before and testify,” he said Tuesday when asked about impeachment. “I don’t think we should be having that conversation. I think we should still pursue the facts.”

Sen. Chris Murphy Christopher (Chris) Scott MurphyDemocratic senator calls for 'more flexible' medical supply chain to counter pandemics The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon GOP chairman to release interim report on Biden probe 'in about a week' MORE (D-Conn.) said colleagues can’t make an informed decision on impeachment without also seeing the information redacted from the Mueller report.

“I have no idea what’s in the redacted portions nor do I know what the underlying material is, so I’m not going to come to a conclusion,” he said.

A Washington Post/ABC News poll published last week found that only 37 percent of respondents said Congress should begin impeachment proceedings, while 56 percent voiced opposition.

There’s some concern among Senate Democrats that pursuing impeachment proceedings could paralyze congressional action on other issues.

Schumer noted to reporters earlier in the day that talk of the Mueller report and impeachment didn’t come up at a White House meeting between Trump and Democratic leaders.

Trump has warned that Democrats should not expect bipartisan dealmaking if they investigate him aggressively, declaring at his State of the Union address, “If there is going to be peace and legislation, there cannot be war and investigation.”

House Democrats, however, insist they can legislate and investigate at the same time.

“Washington is notorious for being able to compartmentalize,” said Rep. Gerry Connolly Gerald (Gerry) Edward ConnollyJudge issues nationwide injunction against Postal Service changes House panel advances bill to ban Postal Service leaders from holding political positions Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' MORE (D-Va.). “I’ve gotten bills passed into law with the most unlikely of allies. Because though we may disagree on 90 percent of everything over here, this 10 percent we agree on, and we are willing to work together.”

Rep. Katherine Clark Katherine Marlea ClarkDemocratic leaders: Supreme Court fight is about ObamaCare Rep. Robin Kelly enters race for Democratic caucus vice chair Clark rolls out endorsements in assistant Speaker race MORE (Mass.), vice chairwoman of the House Democratic Caucus, delivered a similar message, saying Democrats have “been working on two tracks since we took the majority.”

Whether the investigations undermine the infrastructure talks, she said, “is going to be 100 percent up to the president.”

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) on Tuesday called on Democrats to drop impeachment talk and move on to other issues.

“Having just gotten back after a couple of weeks at home, I thought it interesting that I didn’t get a single question about the Mueller report. Most Americans think it’s over, time to move on,” he said.

Jordain Carney and Mike Lillis contributed.