A friend once joked to Joe Lieberman, former senator and vice-presidential nominee, that the Democratic party was like his appendix: it was there but not doing much for him.

“It’s a funny line,” he says by phone from his law office in New York, “but the truth is that it’s more than that because I feel good physically when the Democrats do well – in my terms – and I do get pain when they go off and do things that I don’t agree with.”

Lieberman may be in for a world of pain now. The other Joe – also 79, also a Democratic ex-senator – was expected to share his centrist convictions as US president. Instead Joe Biden as president has surprised friends and foes alike with the scale, scope and audacity of his multi-trillion-dollar agenda.

The Democratic party itself has moved left over the past decade, making it an increasingly awkward fit for Lieberman, who voted for George W Bush’s Iraq war, endorsed Republican John McCain over Barack Obama for president and is still close friends with South Carolina senator Lindsey Graham, the quintessential Republican apologist for Donald Trump.

So it was that in a recent appearance on C-Span to promote his new book, The Centrist Solution, Lieberman was assailed by a caller from Oregon over his “archaic” views and policies that “have done nothing for the poor and the working class”. Another, from Connecticut, upbraided him for the prolonged wars in Afghanistan and Iraq, the deregulation of Wall Street and a crime bill that “put so many Black and Brown people in this country in jail”.

Yet he remains unbowed and undeterred by political currents. Lieberman, co-chair of No Labels, a group focused on bipartisanship, continues to preach a deeply unfashionable gospel of compromise working across the aisle in a country that seems paralysed by a cold civil war.

When he joined the Senate in 1989, he recalls, a typical vote would see around 40 conservatives on one side, 40 liberal on the other, and 20 that were an unpredictable mix. By the time he left in 2013, there was no Democrat with a more conservative voting record than any Republican, and no Republican with a more liberal voting record than any Democrat.

He attributes the polarisation to the gerrymandering of congressional districts, which makes incumbents risk averse, the increasing influence of money in politics – “they expect you to do ideologically what they want you to do” – and the partisanship of both cable news and social media, which encourages politicians to play to their echo chambers.

Lieberman recounts from his Senate experience: “We would want to be able to go home at election time and say, ‘My friends, here’s what I got done for us’. But now people tend to want to go home and say, ‘Oh, here’s what I tried to do except for those bastards in the other party’. That’s a really vicious cycle that takes the country nowhere. The public, certainly the broad middle, is sick of all this.”

This disaffection, Lieberman believes, helps explain why, in 2016, millions of Americans decided to blow it all up by electing an outsider, celebrity businessman Trump. Evidently it did not work as Washington became more poisonous and polarised than ever.

Does the “centre ground” mean anything any more when one party, the Republicans, has veered into far right extremism, for example by embracing Trump’s “big lie” about a stolen election and failing to condemn the 6 January insurrection at the US Capitol?

Lieberman’s answer will strike some as out of touch and trafficking in false equivalence: “The divisive forces in both of our two major parties have moved further away from the centre. But I believe those more extreme segments of both parties are in the minority in both parties.”

“The majority, I’d say, in the Republican party is centre right and in the Democratic party is centre left, and it’s quite possible for them to make their way to the centre and negotiate and come up with centrist solutions. In the book, I’ve tried very hard to distinguish centrism from moderation. Centrism is not an ideology. It’s a strategy for making democracy work.”

He continues: “It takes leaders who are willing to work together across party lines to get something done and, if that doesn’t work, it takes voters who I think are in the majority, certainly the plurality, to demand at election time that the candidates they vote for will work across party lines.”

To many bruised by years of Washington gridlock, this will sound naive.

Lieberman’s support for the 60-vote filibuster, a Senate procedural rule, as one of the last remaining incentives to bipartisanship is out of touch with a new generation of progressives who regard filibuster reform as essential to protecting voting rights and democracy itself.

But he does allow the possibility that the two-system party might no longer be fit for purpose – and that the long awaited, much derided case for a viable third party might become irresistible.

“If one could imagine the Republicans nominating Donald Trump again the president and the Democrats – assuming for a moment that Joe Biden doesn’t run again – nominate somebody further to the left, which is possible as a result of Democratic primaries, wow, there’s going to be a big space in the middle open and somebody will take it,” he says.

“The conditions now are unprecedented in American history. The degree of partisanship and the degree of effective control of the political system by minorities to the right and left in both parties really may open the door to a successful third party campaign for president, perhaps as early as 2024.”

Lieberman has reason to be a student of third party candidacies. In 2000 Ralph Nader’s Green Party polled at less than 3% but was widely blamed for depriving Democratic presidential nominee Al Gore and running mate Lieberman of critical votes in their narrow defeat by Bush and Dick Cheney.

The losing vice-presidential candidate himself, however, is philosophical: “I never blamed Nader because he had the legal right to do what he did and there was some interesting post-election polling that surprisingly indicated that the Nader vote would have divided between Bush and Gore.”

He describes the supreme court’s ruling in favor of Bush in the disputed election as a “miscarriage of justice”, however. A Gore-Lieberman administration is now one of the great historical what-ifs, an alternate timeline that could have shaped the 21st century very differently.

For example, Lieberman points out, Bush oversaw a big and unnecessary tax cut that put America back in deficit territory after three surpluses in a row under Bill Clinton. “I’m confident that President Gore would have felt a responsibility to go into Afghanistan, from which we were attacked [on 11 September 2001], but would he have gone into Iraq? I doubt it. That would have changed history a lot.”

“The other major change would have been obviously that Al Gore was the leading American champion for doing something about climate change. We would have pushed through some reactions to climate change which would have put us in a better, safer situation now.”

Criticized for his resistance to withdrawing from Iraq, Lieberman lost a Democratic primary election for his seat in Connecticut in 2006 only to win election as an independent. Two years later, he again marched to the beat of his own drum by endorsing his old friend McCain, a Republican senator for Arizona, rather than Democratic senator Obama, the first African American nominee of a major party.

He insists: “Surprisingly, neither Barack Obama or Hillary Clinton, both of whom I really knew well, ever asked me for my support. McCain did and I thought, what the hell? He’s my friend, totally capable of being president, and so I don’t regret at all supporting him.”

“We had great areas of agreement on foreign and defense policy but we disagreed a lot. I consider myself a centre left Democrat. He’s a conservative Republican but a maverick so he broke on climate change, he broke for a while on campaign finance reform.”

It later emerged that McCain had wanted Lieberman as his running mate, believing the country ready for a bipartisan ticket, only to be persuaded by his staff to go for the inexperienced, rabble rousing Sarah Palin instead. Another crossroads of history. McCain later admitted it had been a mistake.

Lieberman, the nearly man for a second time, comments: “If McCain had been able to have me as his running mate, I have confidence that we would have done better than he did with Governor Palin. But it’s hard to say that we would have won. Obama was just walking on the mountaintop at that point and Bush 43 was unpopular and the economy was in bad shape, so people really wanted a change.

“And not only was Obama a change in party but he was African American. It was a breakthrough moment for America. I think a lot of people voting for him felt not only that he was the change and capable but that we were going to prove again what we are as a country. So it was an extraordinary moment.”

The close friendship between Lieberman, McCain, who died in 2018, and another senator, Graham of South Carolina, saw them dubbed “the three Amigos”. But where McCain evidently loathed Trump, Graham has defended the former president’s indefensible actions while enjoying his hospitality on the golf course. Does Lieberman ever call him and say, snap out of it?

“Well, we talk a lot. Lindsey will always try, by his nature, to be where he feels he can be effective and so you’ve watched him sometimes be quite close to Trump and at other times be critical. We remain friends. I have nothing negative to say about him because he is my friend but I do think that his great skill ultimately – and I watched it while I was in the Senate – is to be a bridge builder, a bipartisan centrist problem solver.

“At the right moment he will be, I hope, part of the sort of restoration of the Republican party in which he grew up and where his really dear friend – and mine, of course – John McCain was ultimately the nominee. That’s the Republican party Lindsey most naturally fits into.”

It is a party that can still be saved, Lieberman insists. “I don’t think Trump is going to win in 2024 and Republicans who are not tied to him will see that increasingly and people will challenge him, including some who will go back to the regular conservative Republican party, not the party that was so extreme and nasty and willing to ignore the law of the United States.

“I don’t know who it will be. A lot of people are looking at taking him on. It will take some guts. There’s something brewing out there. So, am I optimistic that the more mainstream centrist elements in the Republican party will take over again? I am.”

For their part, Republicans have condemned Biden for campaigning as a centrist but governing as what they perceive as a radical who pushed a $1.9tn coronavirus relief bill, $1.2tn infrastructure deal and $1.75tn social and climate spending package.

Lieberman, who worked with him in the Senate for 24 years, says: “The squad, the further left in the Democratic party, seems to be having influence that is taking him, at least in public perception, further to the left than I certainly thought he was and I’m confident he is now.

“It may be understandable because we’ve just come through an unprecedented crisis because of the pandemic and he wanted to do everything he could to get us back on track. So the bills he supported were bigger than any I ever voted for or that he voted for in the 24 years. But I think we we saw him at his natural best on the bipartisan infrastructure reform bill that just passed and he signed.”

Ever hopeful, Lieberman notes that the president defied progressives by nominating Jerome Powell for a second term as chair of the Federal Reserve. He adds: “Biden is solid. He sees the world realistically and he knows he can’t be Roosevelt or Lyndon Johnson now in part because he doesn’t have the great Democratic majorities that they had.

“And the country, thank God, is not where it was in the Depression, as bad as the pandemic was. The old Joe, which is the real Joe, will be dominant in the next three years of his presidency.”