Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) on Tuesday knocked talk of calling additional impeachment witnesses, arguing that Democrats want the Senate to go "fishing" during the soon-to-start impeachment trial.

"If the existing case is strong, there's no need for the judge and the jury to reopen the investigation. If the existing case is weak, House Democrats should not have impeached in the first place," McConnell said from the Senate floor.

McConnell's comments come as his caucus is locked in an increasingly public fight over impeachment witnesses.

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A small number have suggested they are open to calling witnesses midtrial, but they're getting public pushback from their conservative colleagues, who warn that if Republicans support calling former national security adviser John Bolton John BoltonDiplomacy with China is good for America The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep DOJ launches probe into Bolton book for possible classified information disclosures MORE they also have to support calling witnesses Trump might want such as Hunter Biden or the whistleblower at the center of the House impeachment inquiry.

Democrats are planning to force votes on calling four witnesses, including Bolton and acting White House chief of staff Mick Mulvaney Mick MulvaneyMick Mulvaney to start hedge fund Fauci says positive White House task force reports don't always match what he hears on the ground Bottom line MORE. They need four GOP senators to successfully call a witness.

McConnell, however, argued on Tuesday that demands for additional witnesses "do not show confidence" in the House case.

"The Constitution gives the sole power of impeachment to the House. If a House majority want to impeach a president, the ball is in their court, but they have to do the work," McConnell added.

Senate Minority Leader Charles Schumer Chuck SchumerMcConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt Schumer lashes out at Trump over 'blue states' remark: 'What a disgrace' MORE (D-N.Y.) defended his party's witness request in his own floor speech on Tuesday, arguing that without additional witnesses or documents the trial will be a "sham." During President Clinton's impeachment trial, the Senate voted along party lines to depose three witnesses behind closed doors.

"All we're asking is for the president's own men, his appointees, to come forward and tell their side of the story," Schumer said. "The American people want a fair trial in the Senate. ... The American people will be able to tell the difference between a fair hearing of the facts and a cover up."