Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellDemocratic senator to party: 'A little message discipline wouldn't kill us' House to vote on resolution affirming peaceful transition of power Republican lawyers brush off Trump's election comments MORE (R-Ky.) teed off against the House impeachment inquiry on Tuesday, marking his first comments since Congress returned from its two-week break.

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"House Democrats are finally indulging in their impeachment obsession. Full steam ahead," McConnell said during a speech from the Senate floor, adding that House Speaker Nancy Pelosi Nancy PelosiDemocratic senator to party: 'A little message discipline wouldn't kill us' Overnight Health Care: New wave of COVID-19 cases builds in US | Florida to lift all coronavirus restrictions on restaurants, bars | Trump stirs questions with 0 drug coupon plan Overnight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds MORE (D-Calif.) had "crumbled" to the "left-wing impeachment caucus."

"I don't think many of us were expecting to witness a clinic in terms of fairness or due process. But even by their own partisan standards, House Democrats have already found new ways to lower the bar," McConnell added.

McConnell's comments come as House Democrats are holding near daily closed-door interviews with current and former administration officials as they dig into Trump's effort to get Ukraine to investigate former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE and his son Hunter Biden.

Trump and his allies have lashed out at the investigation and argued that House Democrats must hold a public vote to formally launch an inquiry. Pelosi has said such a vote isn't necessary, though her caucus is expected to discuss that issue at a closed-door meeting later Tuesday.

Republicans are eager for a formal vote, arguing it would force swing-district Democrats to go on the record while bolstering their conference's ability to demand documents as part of an investigation.

McConnell didn't comment on Trump publicly calling on Ukraine and China to investigate the Bidens from the floor on Tuesday. He's remained largely silent on Trump's remarks since before Congress's two-week break.

But he lashed out at Democrats on Tuesday, saying they had "wasted no time throwing fairness and precedent to the wind."

"For all the public hyperventilating over institutional norms that we've heard from House Democrats, it appears they have no intention of letting norms, precedents or basic due process stand in the way as they seek to cancel out a presidency," McConnell added.