As Donald Trump prepared on Tuesday to address the billionaires gathered in Davos, the US Senate prepared to hear opening arguments in an impeachment trial that could remove Trump from the presidency, if not from his seemingly unassailable perch in the public eye.

For only the third time in history, prosecutors sent by the House of Representatives will rise on the Senate floor to charge the president with “high crimes and misdemeanors” and declare that he must be turned out of the White House.

Trump “is the framers’ worst nightmare come to life”, Adam Schiff, chair of the intelligence committee and the lead impeachment prosecutor, wrote in a brief filed Monday, referring to the authors of the US constitution.

Trump was impeached in a party-line vote on two articles, or charges, in the House last month, for abuse of power and obstruction of Congress, relating to accusations that he threatened US national security with his conduct towards Ukraine.

But as his Senate trial got under way in earnest, Trump received a powerful boost of support from the majority leader, Mitch McConnell, who on Monday night unveiled a resolution designed to move the trial forward with unanticipated speed.

The schedule laid out by McConnell would consign key proceedings to late, potentially post-midnight hours and left in doubt whether the Senate would admit evidence gathered in the House – much less call any witnesses to testify about Trump’s conduct.

Chuck Schumer, the top Democrat in the Senate, called the resolution “a national disgrace”.

It is “clear Senator McConnell is hell-bent on making it much more difficult to get witnesses and documents and intent on rushing the trial through”, Schumer said.

Cocooned by the fidelity of a Republican party intolerant of the least criticism of their leader, even as the trial begins Trump appeared to be safe in his post. A two-thirds majority of members present in the Republican-controlled Senate would be required to remove him.

But the Senate trial may hold hidden pitfalls for Trump, including some that could be beyond the power of his sworn allies in the Senate leadership to prevent.

To make their case, Democrats will seek to call witnesses who might change the way the public perceives Trump’s alleged scheme to wield the unique powers of his office for his own political advantage.

But under the McConnell rules, potential witnesses would need to be deposed before testifying at the trial, and individual Senate votes would be required to call the witnesses. It appeared that McConnell had enough votes from his caucus to push the rules package through as soon as the trial convenes on Tuesday afternoon.

Republicans have vowed to prevent witnesses from appearing in order to testify, but just a few temporary defections from that party line would give Democrats the narrow majority required to force witnesses through or obtain new documents.

Presiding at the trial will be John Roberts, chief justice of the US supreme court, who is expected to rule with a light touch but who will have the power to admit evidence or testimony that Trump might prefer omitted.

On the eve of the trial, a dozen lawyers for the president revealed the full scope of their legal strategy, which will follow Trump’s lead in taking a scorched-earth approach to the allegations against him.

In a 110-page legal brief filed with the Senate on Monday, the lawyers called the impeachment “an affront to the constitution and to our democratic institutions” and “a brazenly political act by House Democrats that must be rejected”.

The document attacked the Democrats’ case on constitutional grounds, arguing that the impeachment was invalid because Trump had not been accused of violating a particular law.

But that interpretation of the constitution was unrecognizable to constitutional law experts, many of whom expressed public dismay at what they called the reckless language of the document.

“Their argument is wrong, particularly when they contend that ‘high crimes and misdemeanors’ requires proof of an indictable crime,” Frank O Bowman III, a professor at the University of Missouri school of law and an impeachment expert, told the Guardian in an email.

He continued: “Not true. Never has been, either in England or the US. To argue otherwise, they cherry-pick their sources and ignore the massive body of contrary evidence.”

While skipping past most of Trump’s alleged conduct – all but ignoring the role in the Ukraine scheme of Trump’s main emissary, Rudy Giuliani, and ignoring evidence showing Trump’s role in withholding military aid to Ukraine – the legal document staked out a narrow band of conduct by Trump and advanced familiar defenses of that conduct.

In a July 2019 phone call in which Trump reminded the Ukrainian president, Volodymyr Zelenskiy, that “the United States has been very, very good to Ukraine” and then asked for “a favor”, Trump was motivated by a desire to stamp out internal Ukrainian corruption, the document argued.

“It’s like Presidential tweets reformatted to look like a legal document,” tweeted Orin Kerr, a prominent scholar of constitutional law and law professor at the University of California-Berkeley.

One of the most flagrant assertions in the Trump legal brief, according to scholars, was an attack on subpoenas issued by the House during the impeachment proceedings as “defective”. The White House relied on that reasoning to deny witnesses and testimony to the House inquiry, which prompted the obstruction of Congress charge.

“This is the argument of a monarch,” wrote Schiff, “with no basis in the constitution.”

But as he prepared to depart for Switzerland, Trump got well out ahead of his lawyers on Twitter, in a pattern that could repeat itself during the trial, which is expected to last at least two weeks and could run for much longer.

“They didn’t want John Bolton and others in the House,” Trump tweeted, referring to his former national security adviser, who could recount direct conversations with the president about Ukraine, in testimony that could be damaging.

In fact, the intelligence committee requested in October that Bolton appear to testify, but he declined, threatening the committee with a lawsuit if they attempted to subpoena him.

“No, Mr. President, we did ask John Bolton to testify,” Schiff replied on Twitter. “You ordered him not to, and blocked others, like [acting chief of staff] Mick Mulvaney.

“All Americans know what [sic] a fair trial includes documents and witnesses.

“What are you hiding?”