Pelosi, D-Calif., said the House plans to vote this week to transmit the articles of impeachment to the Senate for the historic trial on charges of abuse of power and obstruction of Congress over Trump's actions toward Ukraine.
Pelosi proposed to submit the indictment when the house was voted on Wednesday and to name the property managers for the case, according to an unauthorized democratic adjutant who discussed the meeting in camera.
It will be only the third impeachment trial in American history.
She warned, "Now the ball is in their court to either do that or pay a price".
The Senate now has 53 Republicans, 45 Democrats and two independents who usually vote with the Democrats.
A senior Democratic aide said McConnell's likely decision not to pursue a motion to dismiss shows McConnell is "desperately trying to keep his members in line". Roy Blunt, a Missouri Republican, who is not up for reelection in 2020.
Trump is confronted with allegations that he has abused power by forcing Ukraine to investigate Democratic rival Joe Biden and subsequently impeding Congress.
The trial could begin this week. While speaking to an global media outlet, Republican Senator Roy Blunt said that there is no interest among the senators for a motion to dismiss the House charges. During the House investigation, Trump ordered key administration officials not to honor subpoenas for their testimony or documents.
That would only require a majority vote.
But a motion to dismiss may not be included in the impeachment rules resolution, because that vote could put Republicans up for reelection in a hard spot and McConnell does not have the 51 votes needed to approve it early in the trial.
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The Clinton resolution referenced by Mr McConnell did not resolve whether witnesses would be called. If four or more Republican senators call for witnesses, it's likely McConnell will be forced to cave and give in to the demands.
"To be using this for a ideal phone call, where the president of that country said there was no pressure whatsoever - did not even know what we were talking about". 'I expect that barring some kind of surprise, I'll be voting in favor of hearing from witnesses after those opening arguments'.
Democrats have been pushing Republicans, who have a slim Senate majority, to consider new testimony, arguing that fresh information has emerged during Pelosi's monthlong delay in transmitting the charges.
McConnell "has signed on to a dismissal resolution". He prefers to partially model Trump's trial based on the trial used in 1999 against the then President Bill Clinton.
Mr Trump has been touting unsubstantiated corruption claims about Mr Biden and his son, Hunter Biden, who served on the board of a Ukraine gas company.
Trump's lawyer Rudy Giuliani has been pursing theories about the Bidens, but other Republicans are cool to embrace his work.
"I am hopeful that we can reach an agreement on how to proceed with the trial that will allow the opportunity for witnesses for both the House managers and the President's counsel if they choose to do so", Ms Collins said.
Trump suggested simply dismissing the charges over the weekend, rather than legitimizing Parliament's charges, which he sees as "hoaxes".
McConnell and other Republican lawmakers have made it clear they want a quick trial in the Senate, where it is widely expected Trump will be acquitted on his two impeachment charges. "To me, it means that we have to take that step back from being hand in glove with the defense, and so I heard what leader McConnell had said, I happened to think that that has further confused the process".