The Senate Republican leader, Mitch McConnell, is proposing to push back the start of Donald Trump’s impeachment trial by a week or more to give the former president time to review the case.

House Democrats who voted to impeach Trump last week for inciting the 6 January Capitol attack have signaled they want a quick trial as President Joe Biden begins his term, saying a full reckoning is necessary before the country – and the Congress – can move on.

But McConnell told his fellow GOP senators on a call Thursday that a short delay would give Trump time to prepare and stand up his legal team, ensuring due process.

The Indiana senator Mike Braun said after the call that the trial might not begin “until sometime mid-February”. He said that was “due to the fact that the process as it occurred in the House evolved so quickly, and that it is not in line with the time you need to prepare for a defense in a Senate trial”.

The timing will be set by the House speaker, Nancy Pelosi, who can trigger the start of the trial when she sends the House charges for “incitement of insurrection” to the Senate, and also by McConnell and the new Senate majority leader, Chuck Schumer, who are in negotiations over how to set up a 50-50 partisan divide in the Senate and the short-term agenda.

Schumer is in charge of the Senate, assuming the majority leader post after Democrats won two new Senate seats in Georgia and Vice-President Kamala Harris was sworn in on Wednesday. But with such a narrow divide, Republicans will have some say over the trial’s procedure.

Democrats are hoping to conduct the proceedings while also passing legislation that is a priority for Biden, including coronavirus relief, but they would need some cooperation from Senate Republicans to do that, as well.

Schumer told reporters on Thursday that he was still negotiating with McConnell on how to conduct the trial, “but make no mistake about it. There will be a trial, there will be a vote, up or down or whether to convict the president.”

Pelosi could send the article to the Senate as soon as Friday. Democrats say the proceedings should move quickly because they were all witnesses to the siege, many of them fleeing for safety as the rioters descended on the Capitol.

“It will be soon, I don’t think it will be long, but we must do it,” Pelosi said on Thursday. She said Trump did not deserve a “get out of jail card” for his historic second impeachment just because he has left office and Biden and others are calling for national unity.

Without the White House counsel’s office to defend him – as it did in his first trial last year – Trump’s allies have been searching for lawyers to argue the former president’s case. Members of his past legal teams have indicated they do not plan to join the effort, but the South Carolina senator Lindsey Graham told GOP colleagues on Thursday that Trump was hiring the South Carolina attorney Butch Bowers, according to a person familiar with the call who was granted anonymity to discuss it. Bowers did not immediately respond to a message Thursday.

Prosecuting the House case will be Pelosi’s nine impeachment managers, who have been regularly meeting to discuss strategy. Pelosi said she would talk to them “in the next few days” about when the Senate might be ready for a trial, indicating the decision could stretch into next week.

Trump told thousands of supporters to “fight like hell” against the election results that Congress was certifying on 6 January just before an angry mob invaded the Capitol and interrupted the count. Five people, including a Capitol police officer, died in the mayhem, and the House impeached the outgoing president a week later, with 10 Republicans joining all Democrats in support.

Pelosi said it would be “harmful to unity” to forget that “people died here on January 6, the attempt to undermine our election, to undermine our democracy, to dishonor our Constitution”.

Following his first impeachment, Trump was acquitted by the Senate in February after his White House legal team, aided by his personal lawyers, aggressively fought the House charges that he had encouraged the president of Ukraine to investigate Biden in exchange for military aid. This time around, Pelosi noted, the House was not seeking to convict the president over private conversations but for a very public insurrection that they experienced themselves and that played out on live television.

“This year the whole world bore witness to the president’s incitement,” Pelosi said.

Dick Durbin of Illinois, the No 2 Senate Democrat, said it was still too early to know how long a trial would take, or if Democrats would want to call witnesses. But he said: “You don’t need to tell us what was going on with the mob scene – we were rushing down the staircase to escape.”

McConnell, who said this week that Trump had “provoked” his supporters before the riot, has not said how he will vote. He told his GOP colleagues that it would be a vote of conscience.