Days before a final vote to impeach Donald Trump is expected in the House over accusations that the president “betrayed the nation by abusing his high office”, Chuck Schumer, the Senate’s top Democrat, is warning that a Senate trial without witnesses would amount to a “cover-up” by the White House.

The demand that John Bolton, the former national security adviser fired by Trump in September, and the acting chief of staff, Mick Mulvaney, should testify was the opening salvo in an effort to force the Republican Senate leader, Mitch McConnell, to negotiate over the proceedings. The two are key eyewitnesses to many of the most contentious elements of the Ukraine scandal.

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“Trials have witnesses. That’s what trials are all about,” Schumer told reporters at a press conference on Monday. “To engage a trial without the facts coming out is to engage in a cover-up.”

The request sets up a bruising clash over the shape and scope of only the third impeachment trial in US history.

The trial, which Schumer proposes should start on 7 January, is now all but certain. The House of Representatives, controlled by the Democrats, is set to vote in favor of two articles of impeachment on Wednesday.

The Democrat-controlled judiciary committee laid out its case for impeachment early on Monday with the release of a 658-page report, charging Trump with placing “his personal, political interests above our national security, our free and fair elections, and our system of checks and balances”.

The committee accused Trump of committing constitutional and criminal bribery by trying to press Ukraine to investigate the former vice-president Joe Biden and the 2016 election as the country’s military aid was held up.

“Applying the constitutional definition of ‘bribery’ here, there can be little doubt that it is satisfied,” the report reads.

Still, the impeachment vote will be difficult for moderate freshman Democrats, especially those who flipped Republican seats that Trump won in 2016. One of those Democrats, the New Jersey congressman Jeff Van Drew, told aides over the weekend that he intends to switch parties. A wave of other “frontline” Democrats began announcing their plans.

At a raucous town hall on Monday that highlighted the deep partisan divide over impeachment, the Michigan congresswoman Elissa Slotkin, a Democrat from a conservative district, explained over shouts and cheers her decision to support articles of impeachment against Trump.

Meanwhile in Washington, Schumer laid out a possible structure based on Bill Clinton’s impeachment in 1999. He pointedly notes that the ground rules on that occasion were approved by a vote of 100-0.

In his letter to McConnell, Schumer writes: “Senate Democrats believe strongly, and I trust Senate Republicans agree, that this trial must be one that is fair, that considers all of the relevant facts … The trial must pass the fairness test with the American people. That is the great challenge for the Senate in the coming weeks.”

But hopes of a similar bipartisan agreement over the likely trial were all but dead in the water before Schumer sent his letter. Republicans have made clear they have no intention of abiding by constitutionally prescribed parameters for the trial, which effectively place senators in the role of jurors.

McConnell, who as the majority leader will have ultimate say over how the trial is conducted, has stated brazenly that Trump will not be convicted and that he will design the trial in consultation with the president – the lead juror in league with the defendant.

“Everything I do during this, I’m coordinating with the White House counsel,” McConnell said last week.

Other senators have indicated they have reached a verdict of acquittal even before the first witness is called.

“I have made up my mind, I’m not trying to pretend to be a fair juror here,” Senator Lindsey Graham, the Trump apologist from South Carolina, has said.

This weekend, footage of Graham speaking in 1999, when he was a House manager in the impeachment of Bill Clinton, made the rounds on social media.

“I have a duty far greater than just getting to the next election,” Graham said in the footage. “Members of the Senate have said, ‘I understand everything there is about this case, and I won’t vote to impeach the president.’ Please allow the facts to do the talking … Don’t decide the case before the case’s end.”

Though the Republicans are in the driving seat, their control is not beyond challenge. Were the Democrats to persuade just four Republicans to vote against party lines they could reach the 51 votes needed to determine some features of the trial.

In an interview with CNN on Monday, Schumer implied that getting those four votes was not out of the question, though he would give no names of potential targets.

“There are a good number of Republicans who are troubled by what the president did,” he said, “who want to see all the facts.”

Speculation has focused on senators including Mitt Romney of Utah, who has criticised Trump relatively strongly, and moderates Susan Collins of Maine, and Lisa Murkowski of Alaska.

Trump faces two articles of impeachment. The first accuses him of misusing his office to bully Ukraine into investigating Joe Biden in a way that would benefit Trump’s re-election campaign; the second charges the president with obstructing Congress by blocking witnesses to impeachment hearings.

Despite the hyper-partisan battle ahead, Schumer’s demand for Bolton and Mulvaney to be called as witnesses could be significant as it goes to the heart of the evidence of “high crimes and misdemeanors” that impeachment is devised to penalise.

Two other key officials have also been requested by the Democrats: Mulvaney’s senior adviser, Robert Blair, and Michael Duffey, associate director for national security at the Office of Management and Budget.

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Evidence already gathered has revealed Bolton’s deep misgivings about the way Trump was pressurising Ukraine for personal political gain, reportedly complaining: “I am not part of whatever drug deal [Trump aides] are cooking up.”

Mulvaney’s testimony would also be potentially critical given his statement in October that there had indeed been quid pro quo with Ukraine. The Trump administration withheld almost $400m in military aid to the country at the same time as demanding an investigation into Biden.

Joan E Greve contributed reporting