The band played On The Road Again. The New York studio audience chanted: “Bernie! Bernie! Bernie!” Senator Bernie Sanders was making his 16th appearance on CBS’s The Late Show with Stephen Colbert – tying the record set by comedian John Oliver.

Colbert confronted his guest with a card bearing a provocative headline, “Joe Biden Is Bernie Sanders”, from a Wall Street Journal column that argued the president will effectively be running for a re-election as a democratic socialist. The host asked Sanders: “Was this news to you?”

With a hearty laugh, Sanders, 81, recalled that, after the 2020 Democratic primary, his team and Biden’s had joined forces to produce an “agenda for working families”. They did not agree on everything but “put together probably the most progressive outline that any president has introduced since FDR” – a reference to Franklin Delano Roosevelt’s New Deal in the 1930s.

Nearly eight years have passed since Sanders, an independent senator from Vermont, launched his first run for US president. The economic populist outsider rocked the establishment as he mounted a fierce challenge to frontrunner Hillary Clinton in the Democratic primary. Sanders lost but put issues such as class inequality, universal healthcare and the negative effects of globalisation in mainstream political discourse.

Four years later, Sanders ran and lost again. But whereas the battle with Clinton had turned bitter, their mutual antipathy palpable, the relationship with Biden proved constructive. The president included progressive voices in his administration and, along with his chief of staff, Ron Klain, committed to keeping the door open to Sanders and his allies.

The upshot has been an agenda more ambitious in scope and scale than many imagined and a Democratic president working more closely with progressives than Jimmy Carter, Bill Clinton or Barack Obama did.

But Sanders aides, alumni and supporters interviewed by the Guardian offered a mixed verdict, welcoming Biden’s faith in government to deliver – a repudiation of Ronald Reagan’s trickle-down economics – while expressing frustration over setbacks on healthcare, progressive taxation and other issues.

Few disputed that Biden and Sanders share an authenticity and do not come over as polished, scripted or elitist. Faiz Shakir, chief political adviser to Sanders, recalls that during the 2020 campaign, many Sanders voters said Biden was their second choice and vice versa.

“Biden has a kind of plainspeak about him,” he said. “That is also the style of Bernie Sanders, to relate with a working-class person, not to suggest that ‘I know more and I’m smarter than you’, which occasionally does happen from the people who have more advanced degrees, become schooled in technocratic talk and start using various abbreviations for government agencies.”

After Biden won the nomination, the president and Sanders appointed six joint taskforces that came up with a 110-page policy document. Shakir described Biden’s team as “a pleasure to work with” and said he had “moved in a progressive direction both during the campaign and as president”.

Now 80, Biden was long perceived as a centrist and moderate who would not challenge the status quo. He represented Delaware for 36 years in the US Senate and served as Barack Obama’s vice-president. He has made much of his belief in bipartisanship and still speaks warmly of Mitch McConnell, the Republican minority leader in the Senate, who has thwarted many liberal dreams.

Yet with a gossamer-thin majority in Congress, Biden has also pulled off four big wins worth trillions of dollars: coronavirus relief, a sweeping infrastructure law, a massive boost to domestic production of computer chips and the biggest climate crisis law in history. He won further goodwill on the left by withdrawing US forces from Afghanistan to end America’s longest war. What happened?

Shakir identifies two major influences. First, Sanders’ insurgent campaigns in 2016 and 2020 built a mass movement that attracted millions of people. “Biden was not clueless as to the need to make sure that if he was going to win, he needed all those people in his tent, and he’s been a good coalition builder in that regard.”

Then there was an accident of history, an opportunity in crisis. “When Covid came along, it just affirmed that to the extent that we needed government solutions to address crises in America, they needed to be progressive. The politics changed in a big way such that people were needing and desiring and wanting government action. As a result he’s been able to pass a bunch of legislation that shows government is going to be a very strong actor on the scene in a way that it hasn’t been in decades.”

Adam Green, co-founder of the Progressive Change Campaign Committee, an ally of Senator Elizabeth Warren, agrees. “The Covid crisis gave Joe Biden a permission structure to think bigger and a bit differently than he did his entire political career and made him more open to fully baked progressive solutions that had been worked on for years and were very fitting in the moment,” he said.

“The idea of helping workers and helping businesses keep workers. The idea of helping parents take care of their kids. The various solutions that were passed in reaction to the crisis were not made up on the fly. They had been percolating for years among progressives and ended up setting the tone for Joe Biden’s entire presidency.”

As the party has shifted left, Biden, an old-school pragmatist, was willing to shift with it. Last year he announced a plan for student loan forgiveness. He has pledged to take on corporate greed and malfeasance, stand with workers at Amazon and elsewhere and revive American manufacturing in left-behind communities.

But it may be less a Damascene conversion than simply slipping into the comfort zone of a self-described “union man” who has been dubbed “blue-collar Joe” because of his humble roots in Scranton, Pennsylvania.

Larry Jacobs, director of the Center for the Study of Politics and Governance at the University of Minnesota, said: “What was most interesting about Biden’s first two years were how many areas he departed from Obama. If you put yourself back into the Vice-President Biden years, you could almost hear Biden’s criticisms of Obama.

“There’s no doubt that for Biden, where he comes from matters a lot. You can see the imprint of ‘I’m from Scranton’ on a lot of his policies. These may be some of the most progressive policies to encourage unions to protect workers that we’ve seen in decades and decades. It’s the kind of stuff that Obama just didn’t make a top priority.”

Even so, Joe Biden is not Bernie Sanders. The president is an avowed capitalist; the senator is currently on tour promoting a book entitled It’s OK to Be Angry About Capitalism.

Donna Brazile, a Democratic strategist who knows both of them, said: “They’re not the same. Just because someone has similar visions of a just and equitable society, we shouldn’t confuse two very different politicians. They’re different people. The society that Bernie wants is a society where everyone gets a living wage and has healthcare. The society that Joe Biden is fighting for is one where it’s equitable and no one is left behind.”

There have undoubtedly been areas where a President Sanders would have gone further. He has long advocated Medicare for all – a single-payer, government-run healthcare programme that would cover all Americans but that Biden never embraced. Sanders’ wishlist also includes taxing Wall Street transactions more aggressively and using those funds to expand free public colleges and universities.

But some of the failures have come at the hands of Congress rather than the White House. Sanders’ fight for a $15 an hour minimum wage fell in the Senate. His $6tn Build Back Better plan to tackle the childcare crisis, make community colleges tuition-fee, tax billionaires, address homelessness and expand vision, hearing and dental care for the elderly was backed by Biden but blocked by Republicans and the Democratic senators Joe Manchin and Kyrsten Sinema.

Congress did pass legislation to invest nearly $400bn in climate and energy measures and make the biggestreforms to national healthcare policy since Obama’s signature Affordable Care Act. But Sanders told the Guardian it was “extremely modest” since it was a long way short of the Medicare for All and $16.3tn “Green New Deal” he campaigned on in 2020.

Some on the left are disappointed by such compromises and want alternatives to Biden in 2024. Norman Solomon, national director or RootsAction.org and organiser of a “Don’t Run Joe” campaign, said: “Given the extreme crises that we face, from climate to income inequality to the fraying of the social fabric to the diminishment of actual healthcare in the post-Covid era, there are signs that Biden to a significant degree is throwing in the towel around Covid, around anything approximating moving towards healthcare inequality. Bernie’s trying to mitigate the slide.”

The next two years could be an uphill battle for the Sanders agenda. Republicans control of the House of Representatives and are intent on paralysing the White House with multiple investigations. Klain, lauded for giving a sympathetic ear to the left, departed as chief of staff earlier this month and was succeeded by Jeff Zients, whose background as a wealthy corporate executive alarms progressives.

Maurice Mitchell, national director of the Working Families party, said: “Joe Biden’s choice of a chief of staff suggests that perhaps he might be listening even less to people like me.

“That simplistic way the Wall Street Journal framed it doesn’t really tell the story of the real debate and contention that’s happening every single day inside the Democratic party and likely inside of that White House around what direction to take the country and to take to the Biden administration. The fact that it’s live means this is a White House that’s organisable but it could be organised in the direction of a Bernie Sanders or in the direction of a Joe Manchin.”