Joe Biden tried to make the best of the fiscal truce he negotiated with Republican House speaker Kevin McCarthy late on Saturday, designed to prevent a potentially devastating default on US debt in little more than a week.

“The agreement represents a compromise, which means not everyone gets what they want,” the US president said. “That’s the responsibility of governing”.

While the pact will cement Biden’s reputation for bipartisan dealmaking, it comes at a cost. For months he had pleaded for Congress to raise the country’s $31.4tn borrowing limit without a fight, only to be drawn into frenzied budget negotiations in Washington that forced him to cut short a trip to Asia.

Many Democrats — particularly those furthest to the left — have grown increasingly unhappy about the terms of the deal as it came together this week, worrying that he was offering too many concessions.

“I think the White House is trying to do a good job and the president’s heart is certainly in the right place,” Sheldon Whitehouse, the Democratic senator from Rhode Island, told the Financial Times ahead of the deal. “The question is, when you’re negotiating with a fanatic who has a hand grenade, the situation can get very precarious.”

The agreement was sealed in a phone call on Saturday evening between McCarthy and Biden. The Republican House speaker announced it before Biden, shortly after 9pm, with a cutting Twitter post. “I just got off the phone with the president a bit ago,” McCarthy wrote. “After he wasted time and refused to negotiate for months, we’ve come to an agreement in principle that is worthy of the American people.”

Biden was able to notch up some policy wins along with conceding some defeats in the pact. Republicans had proposed a rise in the debt limit lasting one year, with spending restrictions in place for a decade. In the end, Biden secured an increase in the borrowing limit until after the next presidential election. Non-defence spending will be roughly flat in fiscal year 2024 then rise by 1 per cent the following year. Biden’s defence budget request will remain intact.

As details of the deal emerged this week, Mark Zandi, chief economist at Moody’s Analytics, said it would not deliver a major blow to the economy. “We estimate it will reduce employment by just over 120,000 at the peak of the impact in late 2024,” Zandi said.

“Not the greatest timing for fiscal restraint as the economy is fragile and recession risks are high, but it is manageable.”

Finalising the agreement with McCarthy required a leap of faith on Biden’s part that the Republican speaker would be able to deliver the support needed to pass the bill when it comes to a vote on the House floor, probably on Wednesday.

While other Republican leaders in the House along with party moderates are likely to embrace the deal, the biggest threat comes from angry conservatives who believe McCarthy watered down their initial proposal too much. “I do not like the ‘deal’ as I understand it from the cheerleading so far,” Chip Roy, the Texas House Republican, tweeted Saturday night.

Ken Buck, a Colorado Republican, said he was “appalled by the debt ceiling surrender”.

“The bottom line is that the US will have $35tn of debt in January, 2025. That is completely unacceptable,” Buck wrote on Twitter.

McCarthy will almost certainly require Democratic votes to pass the deal through the House, given he has a very small majority. That will require Biden to play a key role in the coming days to get it over the line.

Some Democrats have been unhappy with how Biden has handled the crisis at a time when the party’s leftwing is already displeased with what they see as his compromises on immigration and energy policy.

As well as the limits on spending, Democrats have been up in arms at the addition of new restrictions on eligibility for social safety-net programmes, mainly food aid. Although Biden was able to limit the changes and secure a carve out for homeless people and veterans, progressive groups saw it as a harmful concession.

“The deal represents the worst of conservative budget ideology; it cuts investments in workers and families, adds onerous and wasteful new hurdles for families in need of support, and protects the wealthiest Americans and biggest corporations from paying their fair share in taxes,” said Lindsay Owens, executive director of Groundwork Collaborative, a left-leaning economic think-tank.

But the alternative to a deal was unthinkable for Biden. If the package is rejected by Congress, it could plunge financial markets into chaos, threatening the strong labour market and dealing a heavy blow to US economic leadership around the world.

Biden might not be strong enough politically to withstand such a hit. In previous fiscal stand-offs, Democratic administrations successfully portrayed Republicans as fiscal extremists. But mixed polls in recent weeks suggest Biden has no clear edge this time round.

“If there’s a recession as a result of this, the president will receive substantial blame, as will the Republicans,” said Jay Campbell, a pollster at Hart Research. “What happens politically at that point really is anybody’s guess”.

Biden has been pressed by his party to ignore the debt ceiling and keep borrowing on constitutional grounds by invoking the 14th amendment, which states that the validity of US debt “shall not be questioned”.

But his administration has insisted that such a unilateral solution — and other alternatives — would be unworkable and legally risky. Regardless, some critics have suggested that Biden should have been more aggressive with Republicans to force McCarthy to stand down.

Biden has spoken sparingly about the fiscal negotiations in recent days, much less than McCarthy and the Republican negotiators, which helped limit any hostility in the final stretch. Taking a more overtly confrontational posture would have gone against Biden’s nature and hurt the prospects for a deal.

“Biden’s normalcy [and] no drama, that’s the gestalt of the administration,” said one senior Democratic strategist.