The Democratic-controlled House, in a party-line vote, impeached Trump on December 18 on charges of abusing power and obstructing Congress. Trump says he did nothing wrong and has dismissed his impeachment as a partisan bid to undo his 2016 election win.
Republicans, though, have said they will follow the same procedure the chamber followed in 1999 for President Clinton's trial.
Trump's conviction in the trial is highly unlikely, given Republicans' 53-47 control of the Senate, and the high two-thirds vote threshold required to find him guilty.
Pelosi tweeted Monday Trump is afraid to allow key aides to testify.
The Senate is expected to vote to acquit Trump even though some moderate Republicans have bristled over McConnell's reflexive support for the president. It would require a rare rules change similar to the approach McConnell used for Supreme Court confirmations.
She warned: "Do that or pay a price". "What I think is important is we have a vote on whether we need additional documents and witnesses".
House managers would present their case against Trump, and the president's legal team would respond, with senators sitting as jurors.
"Obviously, after saying for months that it was urgent that President Trump be impeached the speaker of the House then sat on the articles for many, many weeks", she said, "Unclear exactly what she believes she accomplished by it".
At least one Republican up for reelection, Sen.
Pelosi said she has not eliminated the possibility of ever subpoenaing and going forward with former national security advisor John Bolton.
Trump has remained committed to blocking any top administration officials, current and former, from testifying. Republican allies led by McConnell, R-Ky., Are ready to deliver acquittal quickly without new testimony.
When pressed during her interview by host George Stephanopoulos on Sunday about whether she is having second thoughts about delaying the articles, Pelosi said no.
The president said he should not bear the "stigma" of accusation because he did nothing wrong. Pelosi said the House vote last month means Trump will be "impeached forever" and "for life". The Senate will be in session six days a week starting at 1 p.m., excluding Sundays, to conduct its trial unless senators vote to institute a different schedule.
McConnell fueled Democratic concerns about dismissing the charges outright when he signed onto a resolution sponsored by Sen. Graham and Sen. Josh Hawley, R-Mo. are leading the effort to dismiss the charges against Trump.
Investigators found Trump withheld about $400 million in military aid while pressuring Ukrainian president Volodymyr Zelensky into launching a pair of investigations that would benefit Trump in the 2020 election.
Senators say if witnesses are allowed, some Republicans may also try to subpoena Biden and his son, Hunter Biden, who served on the board of a gas company in Ukraine while his father was vice president. There is no evidence of wrongdoing by either Biden.
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"One of the things that succeeded in retaining the articles was McConnell's elaboration and the president's desire to hide this", said Schiff, D-Calif, on CBS "Face the Nation". Republicans and Democrats are likely to clash over the issue of whether to call new witnesses. But Pelosi's work is nearly done, unless Trump commits more impeachable high crimes and misdemeanors before Congress becomes focused exclusively on his, and their own, reelection bids.
For example, Fiona Hill, a British-born former White House expert on Russian Federation policy, explained in stark detail how Bolton called efforts towards the Kyiv government by Trump lawyer Rudy Giuliani and others a "drug deal" in which he wanted no part.