A top US Republican on Monday said his first one-on-one talks in months with President Joe Biden to avert a calamitous debt default were "productive" but that there was still no deal.

The White House meeting came after Biden returned from a trip to Asia early to hammer out a deal ahead of the US Treasury's June 1 cut off date for Congress to authorize more borrowing.

"I felt we had a productive discussion. We don't have an agreement yet, but I did feel the discussion was productive in areas (where) we have differences of opinion," House Speaker Kevin McCarthy said after the talks.

McCarthy told reporters that negotiators were going to "work through the night" to move the sides closer and that he and Biden would "talk every day to try to find a way to get this done."

Debt limits are raised periodically to cover repayments on loans that have already been approved and spent, but House Republicans are insisting this time that averting a default must be paired with deep cuts to bring down the country's $31.8 trillion debt.

As they sat down for the meeting, Biden said "I am optimistic we are going to make some progress," adding both sides understood they have "a significant responsibility" to solve the impasse.

'Red line'

The on-again, off-again discussions sputtered through the weekend, with McCarthy's team and White House negotiators meeting for more than two hours on Sunday night and another three on Monday.

Biden and McCarthy also spoke by phone Sunday as the president flew home from a G7 summit in Japan.

Republicans insist on spending less money in fiscal year 2024 than 2023, calling it a "red line."

The White House has offered a freeze for 2024 in exchange for Republicans supporting tax increases for corporations and wealthy Americans but McCarthy has rejected the idea.

The Biden administration has proposed limiting spending on some domestic programs but wants the Pentagon to share in the cuts.

Republicans have pushed for boosted military and border security spending, with major rollbacks to non-defense programs.

Disputes also remain over what a White House official characterized as increasingly hard-line Republican demands for beefed-up work requirements for social welfare programs.

Biden points out that Republicans raised the borrowing cap three times under his predecessor Donald Trump without threatening to default on the country's debt obligations.

If lawmakers fail to raise the borrowing cap, the government will careen into default for the first time in history, with potentially catastrophic results.

Many experts say that in a worst-case scenario global stock markets would melt down as the US economy lurches into a downwards spiral, killing millions of jobs.

June 1 deadline

The president is being pressured by progressives in his party to rely on the US Constitution's 14th Amendment -- which states that the validity of public debt "shall not be questioned" -- to bypass Congress and increase the limit on his own.

But he and Treasury Secretary Janet Yellen cautioned that the courts would not be able to resolve any legal disputes quickly enough to meet the deadline.

Yellen sent a letter to Congress on Monday warning again that the United States could find itself unable to pay its bills as soon as June 1.

Even if McCarthy and Biden can hammer out a broad deal, anything they agree to will need to be shepherded through the House of Representatives, where they face pressure from hardliners on both sides not to make too many concessions.

Further complicating the timeline, the Senate is out this week, while the House is slated to be in recess Friday ahead of Memorial Day weekend.