Joe Biden’s nearly $3tn domestic agenda remains unrealized after an 11th-hour push to rally Democrats around a pared-down package that he framed as historic, failed to close the deal in time for his meeting with world leaders in Rome at the G20 summit.

But after a dramatic Thursday of bold promises and dashed hopes, the House speaker, Nancy Pelosi, was forced to postpone a vote on a $1tn infrastructure bill for a second time in a month, as progressives demanded more assurances that a compromise $1.75tn social policy plan would also pass.

It was a setback – though perhaps only a temporary one – for Democratic leaders, who had hoped to hand the president a legislative victory that he could tout during his six-day trip to Europe for a pair of international economic and climate summits.

The delay underscored the depth of mistrust among Democrats – between the House and Senate, progressives and centrists, leadership and members – after a lengthy negotiating process yielded a plan that was about half the size of Biden’s initial vision.

Biden’s proposal includes substantial investments in childcare, education and health care as well as major initiatives to address climate change that, if enacted, would be the largest action ever taken by the US Congress. Revenue would come from tax hikes on corporations and the wealthy.

But in concessions to centrists like the West Virginia senator Joe Manchin and Arizona senator Kyrsten Sinema, paid family leave, free college tuition and efforts to lower prescription drug prices were stripped from the latest iteration of the plan. Progressives were left disappointed by the cuts but their desire to pass the legislation ultimately held little leverage to force major changes.

In a speech before departing for Europe, Biden acknowledged the bill fell short of his legislative ambitions, but reflected the limits of what was politically possible given Democrats’ narrow governing majorities and unified Republican opposition.

“No one got everything they wanted, including me,” he said. “But that’s what compromise is.”

As lawmakers and activists digested the newly released details of the plan, there seems to be a growing consensus among progressives that, while insufficient, the plan makes critical investments in many of their top priorities, especially in the field of tackling the climate crisis.

“The newly announced Build Back Better Act can be a turning point in America’s fight against the climate crisis – but only if we pass it,” leaders of the climate advocacy group Evergreen Action wrote in a memo on Friday.

Julian Zelizer, a historian at Princeton University, said unified control of the White House and Congress can, perhaps paradoxically, make governing harder. Because these moments are rare and often fleeting, there is a rush by the president and his party to pursue an ambitious, legacy-defining agenda, he said.

“But the challenges of legislating don’t go away,” Zelizer said. “And in some ways, the tensions within the party are exacerbated by the stakes being so high.”

Some have argued that scaling back key programs could make it harder for Americans to feel the impact of the new benefits, despite the substantial size of the legislation. That could make it difficult for Biden, whose approval ratings have slid in recent weeks, to sell the plan he told House Democrats would determine the fate of his presidency and their political futures.