Democrats framed the changes as significant wins and a sign that a few more Republicans could be convinced to buck their party on a second round of witness votes next week.
The votes set the stage for a swift trial that could wrap up in less than two weeks. By Tuesday, ahead of the debate, Senate leaders made additional changes to the trial timeline.
"If you really want to get to the bottom of this, if [the administration is] really challenging the fact that president conditioned $400 million in military aid to an ally at war, if Mick Mulvaney has already said publicly that he's talked to the president about it. don't you think you should hear from him?"
Trump's lawyers, led by Pat Cipollone and Jay Sekulow, appeared to struggle to rebut the Democrat charge, ceding much of their opportunity to defend Trump on television and arguing mostly that the House investigation had been unfair to the president.
House Democrats impeached the Republican president last month on two charges: abuse of power by withholding USA military aid to Ukraine, as he tried to pressure Ukraine into interfering in the 2020 election to help him win, and obstruction of Congress by refusing to cooperate with their investigation. "I've always said I would like to see the voters remove the president, not necessarily the Senate because you don't want to get in a cycle of trying to disqualify each other".
Under McConnell's plan, the opening arguments from the House prosecutors would be limited to 24 hours over two days, meaning that senators could face two 12-hour days to start the trial proceedings.
Senators have taken oaths to act as impartial jurors, hearing arguments for six hours a day, six days a week in a trial presided over by the US Chief Justice, John Roberts.More news: Trump weighs travel ban expansion in coming days
A Senate chamber that is normally mostly empty except for during votes instead had all 100 senators forced to sit at their desks with a pile of impeachment documents and a pad of paper, pencils and cups of water, while a gallery packed with journalists and spectators looked on.
If the Senate votes yes, both sides will have an opportunity to motion to subpoena witnesses, then senators will debate and vote on them. If McConnell is able to prevent 51 senators from voting in favor of witnesses, the trial could be done by the end of next week.
"It's clear Senator McConnell is hell-bent on making it much more hard to get witnesses and documents and intent on rushing the trial through", Schumer said in a statement.
Zoe Lofgren, a Democratic congresswoman on the prosecution team, pointed to historic precedent.
However, Democrats have vowed to object to a speedy trial and pressed for fresh witnesses and documents.
"Not a single [previous] president has categorically refused to co-operate with an impeachment investigation", she said.
"The basic structure we're proposing is just as eminently fair and even-handed", McConnell said.More news: Trump commemorates Martin Luther King Jr. Day with memorial visit
The resolution also says the House impeachment managers will not be able to enter evidence into the trial until after the opening arguments.
Mr. McConnell backed down on both points after facing opposition from his own caucus.
But while some Republicans have said they might eventually vote in favor of having witnesses, for now all remained supportive of the GOP timetable to address that question next week. "I could have told you that in five minutes and saved us all a lot of time".
The first day of debate focused on rules mapped out by McConnell for the trial: three eight-hour days of arguments by the Democratic impeachment managers, and three days again for Trump's legal defense team.
The U.S. Constitution does not spell out what offences a president can or cannot be impeached for, referring to "high crimes and misdemeanors", leaving Congress to decide what exactly those are. He is in the Swiss city of Davos this week for an annual four-day gathering of the World Economic Forum.
"That whole thing is a total hoax", he said.More news: Travel restrictions could be imposed over new virus in China