Warring factions of the Democratic party are bracing themselves for a potentially bruising month of negotiations over the two massive economic and social packages that have reached an impasse in Congress threatening to derail Joe Biden’s first term in office.

With Democratic leaders racing against a new 31 October deadline to pass the legislation, and with pressure building on the White House from both centrist and progressive wings of the party, the centerpiece of Biden’s agenda now hangs in the balance. Democratic prospects in next year’s midterm elections are also at stake.

The outcome of the current party wrangling will determine the fate of both the $1tn public works measure which has garnered bipartisan support and the larger $3.5tn social and environmental package which Democratic leaders are hoping to drive through Congress unilaterally.

Pramila Jayapal, the head of the progressive caucus which is demanding that both bills are linked in order to protect the larger social policy overhaul, indicated on CNN’s State of the Union on Sunday that her side of the negotiations is prepared for compromise. Though she declined to give a figure for the size of the package that progressives would accept, she suggested that $1.5tn would be unacceptable.

She said of a reduced $1.5tn deal, “that’s not going to happen. That’s too small to get our priorities in. It’s going to be somewhere between $1.5tn and $3.5tn, and the White House is working on that.”

Jayapal, who represents the Seattle area of Washington state in the House, said that progressives were looking at options for whittling down the scale of the social policy measure, including reducing the timescale of the provisions from their current 10 years and ditching some lesser items. She said she was not in favor of means testing any new benefits, as suggested by some centrist Democrats, but added: “Let’s see, the negotiations are just starting.”

Jayapal’s indication that the progressive wing is now ready to talk numbers will hearten White House negotiators as they begin the epic task of trying to reach a compromise that works for both rival factions of the party. On Friday Biden made a rare visit to Capitol Hill to calm nerves and try and find a way forward.

He effectively sided with progressives, telling House Democrats that the two bills had to be considered together and not apart as centrists prefer. But he also gave the progressive caucus a clear message that the $3.5tn package would have to be diminished, signaling a range between $1.9tn and $2.3tn.

At the end of the visit Biden put a brave face on the standoff which is holding his presidency hostage. He said: “It doesn’t matter whether it’s in six minutes, six days, or six weeks – we’re going to get it done.”

Several of the most critical pledges that Biden made to the American people in the course of the 2020 presidential election are contained in the $3.5tn overhaul. They include measures to tackle the climate crisis, universal pre-kindergarten education, childcare support, paid medical and family leave, and an extension of federal payments to families with children.

By Sunday it had become clear that the desire of the centrist wing of the Democratic party to pass the $1tn infrastructure bill by decoupling it from the larger social and environmental package had come unstuck due to progressive opposition.

Equally, the hope of progressives to pass the full $3.5tn plan, which some have likened to the 1930s New Deal, has also ground to a halt given the resistance of centrist Democrats including senators Joe Manchin from West Virginia and Kyrsten Sinema from Arizona.

Over the weekend Sinema issued a scathing response to last week’s decision by the House speaker Nancy Pelosi to delay a vote on the infrastructure bill until 31 October to buy time for a compromise to be reached.

In a statement she called the decision “inexcusable”. Calling the move by progressives “an ineffective stunt”, she said: “I do not trade my vote for political favors – I vote based only on what is best for my state and the country.”

Some of the most sensitive negotiations over the coming days are likely to take place in the Senate. With the chamber deadlocked 50:50, Democratic leaders cannot afford to lose even one vote which is why Sinema and Manchin are in such a powerful position.

Dick Durbin, the Senate majority whip, told CNN’s State of the Union on Sunday that he and other Democratic leaders were looking at the priorities. “We listen very carefully to every single member – every vote counts in getting to this majority – and concessions will be made, we’re certain of that.”

Durbin said the overriding dilemma was whether to shave down every component of the massive $3.5tn package, or to focus on just the most important elements and let the rest fall by the wayside. The senator from Illinois indicated that support for child care was one item he would not be prepared to jeopardize, though he said other aspects of the measure could be “scaled in a different way”.