Donald Trump’s legal team entered the second day of his impeachment trial on Wednesday on the back foot after a debut performance that was widely panned by Republican senators, including some of the former US president’s closest allies.

The first day of Trump’s trial kicked off on Tuesday with a powerful opening argument from Democratic impeachment managers acting as de facto prosecutors, who relied heavily on video footage that tried to tie the deadly January siege on the US Capitol to the former president’s words and actions.

Trump’s lawyers appeared to struggle to respond during a subsequent four-hour debate that was intended to settle the question of whether it is constitutional to try a former president once he has left office.

Their meandering performance prompted one Republican senator, who backed Trump on the constitutionality question in a vote last month, to switch sides and vote with Democrats in affirming that the trial was indeed constitutional and that the trial should proceed.

Bill Cassidy, a Republican senator from the deep red state of Louisiana, attributed his change of heart to the performance of Trump’s lawyers, Bruce Castor Jr and David Schoen, who he described as “disorganised”.

“They did everything they could but to talk about the question at hand, and, when they talked about it, they kind of glided over, almost as if they were embarrassed of their arguments,” Cassidy said. “As an impartial juror, I’m going to vote for the side that did the good job.”

Even some of Trump’s staunchest allies in the Senate said they were disappointed by his legal team, including Lindsey Graham from South Carolina and Ted Cruz from Texas.

“It took a long time to get to where I think the meat of the question is,” Graham said. “I thought I knew where [Castor] was going, I really didn’t know where he was going.”

Cruz added: “I don’t think the lawyers did the most effective job.”

The performance of Trump’s lawyers is unlikely to make much difference to the odds of the former president being convicted, which remain slim. The vast majority of Republicans voted to back the president on the constitutionality question, with just Cassidy and five other Republican senators voting in favour of the trial proceeding.

The overall vote on proceeding with the trial was 56-44 in favour, after all Democratic senators signalled the process was constitutional. But a conviction would require two-thirds of the upper chamber of Congress to vote against the former president.

“Enough [Republican senators] have said that this process is unconstitutional for us to know exactly what’s going to happen now . . . if you believe that this is unconstitutional, then you cannot convict him . . . game over,” said Doug Heye, a Republican strategist.

However, if Trump’s lawyers are unable to sharpen their arguments during the remainder of the trial, it could complicate efforts by the Republican party to acquit the former president while winning back the support of voters who are outraged by the attack on the US Capitol.

Ford O’Connell, a Trump ally and former Republican congressional candidate, said Democrats were “trying to . . . prey upon the horrors of what happened in the Capitol in an effort to paint all Republican voters as extremists and to prevent Donald Trump from ever running for president in the future”.

“They see the political game here,” he added.

Trump is both the first president to be impeached twice, and also the first former president to face a Senate trial.

His lawyers’ presentation started with an unwieldy opening statement from Castor. Schoen wrapped up with a tearful rendition of a poem by Henry Wadsworth Longfellow, “The Building of the Ship”.

In response to a question from reporters about Cassidy’s criticisms, Schoen replied: “I’m sorry he felt that way — have to do better next time.”

The fiercest criticism was reserved for Castor, whose rambling speech made little mention of the constitutionality question at hand. At one point, he acknowledged that Trump lost November’s presidential election, something that is sure to infuriate his client, who has refused to concede defeat.

John Cornyn, a Republican senator from Texas, said Castor “rambled on and on and on and didn’t really address the constitutional argument”.

“I’ve seen a lot of lawyers and a lot of arguments and that was . . . not one of the finest I’ve seen,” he added.

Castor’s performance was also given poor marks by moderate Republican senators who are seen as more minded to convict the former president.

Susan Collins from Maine said she was “perplexed” by Castor, adding he “did not seem to make any arguments at all, which was an unusual approach to take”.

Lisa Murkowski from Alaska said she was “really stunned”, adding: “I couldn’t figure out where he was going.”

Jamie Raskin, the Democratic congressman from Maryland who is acting as lead impeachment manager, said Cassidy’s vote indicated that Republicans were willing to vote against the former president.

“We were told that it would be completely partisan and locked from the last vote, and it wasn’t,” he told reporters after Tuesday’s debate. “People’s minds are open.”