Washington (CNN) Some Democrats are raising concerns about Senate Majority Leader Mitch McConnell's statement that he will coordinate closely with the White House on the looming Senate impeachment trial , with one House Democrat saying the Kentucky Republican should recuse himself entirely.

"He's working hand in hand with the White House, with the President's attorney, and yet we're supposed to expect him to manage a fair and impartial trial?" said Florida Democratic Rep. Val Demings when asked about McConnell's remarks. "I think he should recuse himself."

Democratic Rep. Pramila Jayapal of Washington called the coordination "ridiculous."

"I think it is outrageous for the chief juror who is organizing the trial to be coordinating with the defendant," Jayapal told reporters.

Under the Constitution, it's up to the House to charge the President with impeachment, and the Senate to convict or acquit -- making senators, including McConnell, the de facto jury.

The House Judiciary Committee on Friday approved articles of impeachment against the President, paving the way for the final floor vote expected next week. That will set up the Senate trial, for which senators are now gearing up.

Democrats wield majority control in the House, but Republicans hold a majority in the Senate.

Some Senate Republicans have been careful not to tip their hands ahead of the expected trial, but many have been vocal in saying that they do not believe the Ukraine scandal rises to the level of impeachment.

McConnell himself said on Fox News on Thursday, "We all know how it's going to end. There is no chance the President is going to be removed from office."

It would take 67 votes in the Senate to remove Trump, so with Republicans holding 53 seats, the President is a virtually lock to be acquitted.

A Senate trial is dictated by what ideas -- for length, or structure or witnesses -- can obtain the support of at least 51 senators. But as majority leader, McConnell does have more power than rank-and-file senators to shape the process.

He told Fox News' Sean Hannity on Thursday night that there will "be no difference between the President's position and our position as to how to handle this."

"Everything I do during this, I will be coordinating with White House counsel," McConnell said.

McConnell and Trump's top lawyer sketched out a plan Thursday, prior to the Fox News interview, to coordinate closely for an impeachment trial. Still, no agreement was reached on an issue where Trump and McConnell diverge. Trump has repeatedly said he wants witnesses at the Senate impeachment trial. McConnell has privately indicated he wants to avoid witnesses out of concern for the political and institutional fallout they might bring.

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Publicly, at least, McConnell was all-in with Trump in his interview, noting he was "going to take my cues from the President's lawyers."

Speaking in Frankfort, Kentucky, on Friday, McConnell addressed the subject again, saying that during the impeachment proceedings against Bill Clinton, the then-President and Senate Democrats coordinated.

"It was done during the Clinton impeachment as well," McConnell said. "Not surprisingly, President Clinton and the Democrats in the Senate were coordinating their strategy. We're on the same side."

Former Sen. Tom Daschle, who was Senate Democratic leader during the Clinton impeachment trial, told CNN's Dana Bash on Friday that while he did not personally talk to Clinton in preparing for the impeachment trial, his staff was in constant coordination with senior White House officials about it.

"There are so many moving parts," Daschle said, referring to coordinating the House managers and White House counsel's office and 100 senators, that they had no choice.

Daschle said he does not fault McConnell for his remarks on Fox News Thursday night about coordination.

"That's the way it is now," Daschle said. "It's different."

He added that, in retrospect, his decision to not speak to Clinton "was probably a little myopic," but added there was more to it for him than just being a juror in the President's trial.

Daschle said he "had been through a lot of highs and lows," with Clinton on the substance of what he was impeached for: having an affair with an intern and then lying about it under oath.

Democratic Rep. Jamie Raskin of Maryland said on Friday morning, however, that he "couldn't believe it" and had to see it with his own eyes that McConnell said he was coordinating each step of the process with the White House.

"That is a complete surrender of the constitutional duties and prerogatives of the Senate, essentially turning them over to the White House," Raskin said.

"Let's hope that there's sufficient clamor within the Senate and within the country to make him rethink this idea of coordinating strategy with the defendant in the case: the President," Raskin said. "This is essentially a constitutional defendant, and he's a defendant because we have voted to send an indictment articles of impeachment to the Senate because of the high crimes and misdemeanors."