After emergency talks at the White House, Republican congressional leaders have begun to sound hopeful that a deal to raise the US debt ceiling is within reach.
But House of Representatives Speaker Kevin McCarthy told reporters the two sides are still far apart.
The standoff has forced President Joe Biden to cut short a foreign trip.
Without a deal, the US could enter a calamitous default on its $31.4tr (£25tr) debt as soon as 1 June.
Mr Biden said Tuesday’s hour-long Oval Office meeting was “good, productive”, sounding upbeat about the prospects of an agreement.
Mr McCarthy told reporters he believed a deal was possible by the end of this week.
He told reporters a Biden-appointed representative would negotiate directly with his staff, which he said was a sign that “the structure of how we negotiate has improved”.
A number of senior Democrats were also at the talks, including Vice-President Kamala Harris, Senate Majority Leader Chuck Schumer and House Minority Leader Hakeem Jeffries.
In exchange for support for raising the debt ceiling, Republican leaders are demanding budget cuts. They also want tougher work requirements on government aid recipients.
Citing sources familiar with the talks, the Associated Press news agency reports that this idea was “resoundingly” rejected by House Democrats at another meeting earlier on Tuesday.
President Biden has repeatedly said that a potential debt default and budgetary issues should be separate.
The president is due to fly to the G7 summit in Japan on Wednesday. He was then expected to head to Papua New Guinea for talks on regional security and to Australia for a meeting of the “Quad” alongside leaders from India, Japan and Australia.
But he will now return after the 19-21 May summit in Hiroshima ends to “ensure that Congress takes action” to avert a default, the White House said in a statement.
Reaching the debt ceiling would mean the US government is unable to borrow any more money.
A default – which would be a first in US history – could upend global financial markets and shatter trust in America’s political ability to pay its bills.
Experts have warned it could also see the US spiral into recession and stoke unemployment.
Treasury Secretary Janet Yellen said at an event on Tuesday that “a US default would generate an economic and financial catastrophe”.
Meanwhile, White House National Security Council spokesman John Kirby said: “There’s countries like Russia and China that would love nothing more than for us to default.”
A deal to avoid this scenario has so far proven elusive. In April, Republicans proposed an agreement that would suspend the debt limit by $1.5tn or until 31 March, whichever comes first.
In exchange, they would maintain spending at key government agencies at 2022 levels for the next financial year and limit spending growth to 1% annually over the next 10 years.
They argued this would lead to $4.8tn in savings.
The proposal, however, would scupper several of Mr Biden’s legislative priorities, including student loan forgiveness.
The last time the US was approaching a default in 2011, lawmakers struck a deal hours before the deadline.
That standoff led to a downgrade in the US credit rating, sent the stock market plummeting and increased the government’s borrowing costs.
“Nobody should use default as a hostage,” Senate Majority Leader Chuck Schumer said at the US Capitol on Tuesday. “The consequences would be devastating for America.”
The US debt ceiling has been raised, extended or revised 78 times since 1960.