By Moira Warburton, Nandita Bose and Gram Slattery

WASHINGTON Negotiators for Democratic President Joe Biden and Republican Speaker Kevin McCarthy were expected to reconvene on Wednesday morning, a source familiar with the matter said, seeking a deal to raise the United States' $31.4 trillion debt ceiling and avoid a catastrophic default.

With just over a week left before the deadline, Biden and House of Representatives Speaker Kevin McCarthy remain deeply divided on how to move forward.

Republicans are pushing for sharp spending cuts while Democrats are offering to keep spending flat, instead using new taxes to help reduce the federal government's debt.

The months-long standoff has spooked Wall Street, weighing on U.S. stocks and pushing the nation's cost of borrowing higher. The Treasury Department has warned it could run short of cash to meet all its needs as soon as June 1.

But Biden and McCarthy's negotiating teams, who reported no significant progress after a two-hour meeting at the Capitol on Tuesday, face an even tighter timeline as it could easily take a week to write any deal into legislation and pass it through the narrowly divided Congress.

"The biggest gap we have is the funding issue," said McCarthy's lead negotiator, Representative Garret Graves, after Tuesday's talks. Republicans want to cut spending for the 2024 fiscal year beginning in October back to 2022 levels, while Democrats have pushed to hold it steady at this year's rate.

White House spokesperson Karine Jean-Pierre called the talks "incredibly tough."

"Both sides have to understand that they're not going to get everything that they want," Jean-Pierre said at a briefing.

Negotiators differ over Republicans proposals to impose new work requirements on benefits programs for low-income Americans, loosening energy permitting rules and clawing back some unspent funds Congress authorized to fight the COVID pandemic.

A source familiar with the White House's negotiations said Biden is "willing to meet the Speaker halfway" and has offered a compromise, which includes a spending freeze, rescinding significant unspent COVID relief funds and a two-year cap on spending in line with previous bipartisan budget agreements.

The source said McCarthy "claims he wants to negotiate, but today he said the only concession he is willing to make is to prevent default — a basic Constitutional responsibility of his job."

Congress regularly needs to raise the nation's self-imposed debt limit to cover the cost of spending and tax cuts it has already approved. It did so three times during Republican Donald Trump's four years in the White House without triggering a similar standoff.

The last time the federal government came this close to default was in 2011, with a similar power divide in Washington - a Democratic president and Senate majority and a Republican-controlled House.

Each party also faces opposition to the talks from within, with hardline Republicans insisting on the sharp spending cuts they passed in a House bill last month and progressive Democrats opposed to spending cuts or new work requirements.

Biden spent months saying he would not negotiate on raising the debt limit only to reverse course and begin talks with McCarthy in the last few weeks.

(Editing by Scott Malone and Lincoln Feast.)