Democratic senators said on Tuesday that the Senate should oppose Supreme Court nominee Brett Kavanaugh if he doesn't agree to recuse himself from legal cases tied to 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 Russia probe.

"I'm a 'no' on this nominee. My colleagues should be a 'no' on this nominee unless Judge Kavanaugh specifically commits that he will recuse himself on any issues that involve 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's personal financial dealings or the special counsel," Sen. Richard Blumenthal (D-Conn.) said during a rally outside the Supreme Court.

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He added that Kavanaugh would be the "swing vote" on cases deciding if Trump could pardon himself or if a sitting president could be indicted or forced to appear before a grand jury.

Trump has repeatedly denied wrongdoing and decried Mueller's investigation into Russian influence in the 2016 presidential election as a "witch hunt."

Trump announced on Monday evening that he was nominating Kavanaugh to replace retiring Justice Anthony Kennedy on the Supreme Court.

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 (N.J.), who is considered a 2020 presidential contender, said he and his fellow Democratic colleagues on the Senate Judiciary Committee plan to ask Kavanaugh whether he’ll recuse himself from matters related to Mueller’s Russia probe if they come before the high court.

“If you just put this fact pattern down to any senator five years ago, just said the president of the United States is under investigation in which there have been over 70 charges filed, over 20-plus people and corporations have been charged, over five people already guilty pleas, one person already sentenced … I guarantee you you’d get senators [who would] say they would not let that president do what he’s doing right now, which is give himself immunity for any issues that come before the Supreme Court,” he said.

“I do not think he should be on the court,” Booker added.

White House deputy press secretary Raj Shah declined to comment when asked by Bloomberg News whether Kavanaugh should recuse himself from issues related to the Mueller probe.

Shah did not respond to a request for comment from The Hill.

Democrats don't have the ability to block Kavanaugh's nomination on their own because Supreme Court nominees only need a simple majority for confirmation in the Senate.

But they're still building their case against Kavanaugh as they try to win over at least two GOP senators, highlighting the nominee's potential impact on Mueller's probe into the 2016 election and possible collusion between Moscow and the Trump campaign.

Democrats are seizing on a 2009 law review article Kavanaugh wrote, in which he said it would be a distraction for a sitting president to be indicted.

"I believe it vital that the President be able to focus on his never-ending tasks with as few distractions as possible," Kavanaugh wrote at the time. "The country wants the President to be ‘one of us’ who bears the same responsibilities of citizenship that all share. But I believe that the President should be excused from some of the burdens of ordinary citizenship while serving in office."

He added that an indictment and trial would "would cripple the federal government."

Updated at 12:38 p.m.