Alexandria Ocasio-Cortez cannot have been surprised that wearing a “Tax the Rich” dress to New York’s Met gala would trigger performative outrage from the right. But it also earned blowback from closer to home.

Eric Adams, a Black police veteran who won the party’s mayoral primary by appealing to its centre, argued that “when you talk about just blanketly saying ‘tax the rich’ in this city”, it would potentially drive away firefighters, teachers and other taxpayers on whom the city depends. He advocated cutting wasteful spending instead.

The pro-business Adams and the democratic socialist congresswoman are two faces of a 193-year-old Democratic party confronting fundamental questions about what it stands for and what it wants to be. While Democrats have moved left on both economic and social issues since the 1990s, this remains a broad and unwieldy coalition by global standards.

Now its diverse and at times discordant voices in Washington are imperiling the agenda of Joe Biden, a longtime centrist who has nevertheless embraced some of the radically transformative ambitions of past Democratic giants such as Franklin Roosevelt and Lyndon Johnson.

Divisions between progressives and moderates in Congress are threatening to scuttle a $3.5tn social spending program, which includes childcare, education and green energy measures, and a $1tn bipartisan infrastructure bill that has passed the Senate and is pending in the House of Representatives.

“Unfortunately for us, at a time when it’s so very important for Democrats to make it clear to the people that we serve where we stand, we couldn’t be more inconsistent with our values right now,” said Yvette Simpson, chief executive of the progressive group Democracy for America. “We can’t get all on the same page to get this done.”

For four years of the Republican Donald Trump’s presidency, Democrats of all stripes united against a common political foe. Since January, however, they have controlled all the levers of power – with House and Senate majorities so razor-thin that every disagreement is thrown into sharp relief against staunch Republican opposition.

Democrats cannot afford to lose more than three votes in the House, and none in the Senate, if they are to pass the social package that has earned comparisons with Roosevelt’s “New Deal” and Johnson’s “Great Society” in its reassertion of government’s power to improve lives.

There is added pressure from the expectation that Republicans are likely to win back the House and possibly the Senate in midterm elections in November of next year. The clock is ticking.

Moderate Democrats back a vote on the $1tn bill for roads, bridges, ports and broadband connections scheduled for the House on Monday. But they have also raised objections to the size of the $3.5tn social spending package, warning against government overreach that will drive up the national debt.

Senator Joe Manchin, who represents heavily Republican West Virginia, has said he will not vote for $3.5trn, preferring instead a total of $1tn to $1.5tn. His Senate colleague, Kyrsten Sinema of Arizona, also wants to trim the cost.

But progressives have vowed to defend the price tag of $3.5tn over 10 years, having already come down from $6tn. They have also said they will not vote for the infrastructure plan without first passing the social spending program, using a manoeuver called “reconciliation,” which avoids the Senate requirement for a supermajority.

Progressives argue that opinion polls show broad bipartisan support for the plan and accuse the moderates of being beholden to corporate interests. Manchin, for example, owns a big stake in a private coal brokerage and his election campaigns have received donations from lobbyists for the oil giant Exxon.

Simpson said: “If we have certain members of our caucus who want to take money from Big Pharma, Big Oil, Big ‘insert name here’, then we’re never going to have a Democratic majority that’s willing to actually serve real people first.”

She added: “It’s really not Democrat versus Republican. It’s the ultra wealthy and the corporations versus all the rest of us because a bill like this in the midst of a pandemic should be very easy to pass. This is a part of Biden’s agenda. It’s actually already a compromise position because progressives wanted way more.”

The scale of ambition is a marker of how far the party has journeyed since, from the ashes of a third consecutive election defeat in 1988, it turned to Arkansas governor Bill Clinton to lead the “New Democrats” (later an inspiration for Tony Blair’s New Labour) to the political centre ground and back to the White House.

Al From, who founded the Democratic Leadership Council in 1985 and handpicked Clinton for the job, is still putting the case for centrism. He points out that Biden comfortably beat Senator Bernie Sanders, a democratic socialist, in last year’s primary and contends that the significance of progressives is “exaggerated” by cable news networks and Twitter.

From also notes that the six progressives who comprise “the squad” in the House are from safe Democratic strongholds, whereas the moderates are from competitive swing districts. “The voters that are going to decide who’s controlling the Congress are probably going to be suburban voters and college graduates, and women are going to be key to that also,” he said. “The suburban voters tend to be more fiscally moderate.

“The vote on the $3.5trn bill is automatic for the progressive caucus because they want to spend all the money in the world. But for the moderates, it may be an election deciding vote because the constituencies that they need to win often vote Republican and tend to be more conservative on economic issues. Part of what this fight is about goes back to who you represent and whose votes you need to get elected.”

From cautioned against viewing the debate as evidence a Democratic identity crisis, however. “We’ve always been a coalition party,” he added. “We’ve always been a very broad tent stretched all across the spectrum. It’s probably less now, in terms of the breadth of a party, that it has been historically. Thirty or 40 years ago it was even a lot more divided.”

The current impasse has led to some terse exchanges on Capitol Hill and forced Biden, a 36-year veteran of the Senate, to step in this week by hosting both moderates and progressives for talks at the White House. Much also depends on Nancy Pelosi, the House speaker, and Chuck Schumer, the Senate majority leader, displaying their political chess-playing skills.

It is a sign of progressive gains in recent years that Pelosi and Schumer have expressed support for their goals and that Sanders is now chairman of the influential Senate budget committee (he has warned plainly: “No infrastructure bill without the $3.5tn reconciliation bill.”) Biden, a surprise radical at 78, appears to have set the tone for the party.

Matt Bennett, executive vice-president for public affairs at the Third Way thinktank and a former official in the Clinton White House, said: “When your party has the White House, you have an identity and the identity is personified by the president for good or bad.

“Republicans for a time were having an identity crisis under Trump because you saw people exiting the party in large numbers, particularly their intelligentsia. The core of the Bush administration announced they were opposed to a Republican president. That’s an identity crisis. What we’re having is a debate.”

It is a debate set to rage on, further complicated by Republicans reasserting their vow not to help Democrats raise the federal government’s debt limit before a mid-October deadline. The various moving parts look set to make or break Biden’s presidency and prove a defining chapter in the Democratic party’s long history.

Leah Greenberg, co-founder and co-executive director of the Indivisible Project, a progressive nonprofit organisation, said: “There’s a cohesive identity of a big faction of the Democratic party, ranging from the president to progressives; it really shows the total ideological and political incoherence of the conservative Democratic bloc.

“They just have random feelings about the price tag, various preferences around not taxing the rich, not actually limiting corporate power, et cetera. The fight here is not even between moderates and progressives. It’s between people who are trying to deliver on the full Democratic agenda and people who are trying to take bites out of it for complicated, incoherent reasons, usually involving delivering for corporate donors.”

And while Manchin and Ocasio-Cortez belonging to the same party might seem a recipe for political dysfunction, it is still in a different league from events across the aisle over the past decade.

Greenberg added: “The dominant story in American politics is not necessarily the changes in the Democratic party. It is the fact that the Republican party has just been completely unmoored from political reality, from any commitment to democracy, and is hell bent on using the tools it has in order to maintain and exert power.”