President Joe Biden and House Speaker Kevin McCarthy failed late Monday to reach an agreement on raising U.S.'s borrowing limit in time to avert a potentially chaotic federal default. However, both said they had a "productive" debt ceiling discussion late Monday.

It marked a crucial moment for the Democratic president and the top congressional Republican, just 10 days before a looming deadline that could sink the U.S. economy.

In her third letter to Congress in three weeks, Treasury Secretary Janet Yellen said "it is highly likely" the government will be unable to pay all the nation's bills as soon as June 1 without congressional action to raise the $31.4 trillion debt ceiling.

Such an unprecedented default, which would mark the first ever for the U.S., would be financially damaging for many Americans and others around the world relying on U.S. stability, sending shockwaves through the global economy.

Each side praised the other's seriousness, but fundamental differences remained. They are at odds over how to trim annual budget deficits. Republicans are determined to cut spending, while Biden's team offered to hold spending levels flat. Biden wants to increase some taxes on the wealthiest Americans and some big companies, but McCarthy said early on that is out of the question.

"The time of spending, just spending more money in America and the government is wrong," McCarthy said after the Oval Office meeting.

In a brief post-meeting statement, Biden called the session productive but merely added that he, McCarthy, and their lead negotiators "will continue to discuss the path forward." Upbeat, McCarthy said their teams would work "through the night."

Biden said all agreed that "default is not really on the table."

Though there is no agreement on basic issues, the contours of a deal seem within reach. A budget deal would unlock a separate vote to lift the debt ceiling, now $31 trillion, to allow more borrowing.

Negotiations are focused on finding a compromise over a 2024 budget year cap that would be key to resolving the standoff. Republicans insisted next year's spending be less than it is now, but the White House instead offered to hold spending flat at current 2023 numbers.

Republicans initially sought to roll back next year's spending to 2022 levels, and impose 1% caps on spending growth for 10 years, though a later proposal narrowed that to about six years. The White House wants a two-year budget deal, keeping 2024 spending flat. They proposed a 1% cap on spending growth for 2025, according to a person familiar with the talks, and granted anonymity to discuss them.

A compromise on those topline spending levels would enable McCarthy to deliver for conservatives, while not being so severe that it would chase off the Democratic votes that would be needed in the divided Congress to pass any bill.

"We're going to find a baseline that we agree to that will be less than what we spent this year," McCarthy said back at the Capitol.

Time is growing short. The House speaker promised lawmakers he would abide by the rule to post any bill for 72 hours before voting, making any action doubtful until the end of the week – just days before the potential deadline. The Senate would also have to pass the package before it could go to Biden's desk to be signed into law.

After a weekend of start-stop talks, both Biden and McCarthy declared a need to close out a compromise deal. U.S. financial markets turned down last week after negotiations paused amid a jittery economy.

Biden and McCarthy spoke on the phone Sunday while the president was returning home on Air Force One after the Group of Seven (G-7) summit in Japan.

Biden used his concluding news conference in Hiroshima, Japan, to say he had done his part by agreeing to spend cuts and to warn, "It's time for Republicans to accept that there is no deal to be made solely, solely, on their partisan terms."

"Now it's time for the other side to move from their extreme position," he said.

The call between the two revived talks and negotiators met for 2 1/2 hours at the Capitol late Sunday evening. Negotiators were back at it again for nearly three hours Monday morning ahead of the session at the White House. The White House team returned late Monday night for nearly two hours at the Capitol, leaving before midnight upbeat but with little comment.

But McCarthy continued to blame Biden for having refused to engage earlier on the debt ceiling, an issue that is often linked to the federal budget.

GOP lawmakers have been holding tight to demands for sharper spending cuts with caps on future spending, rejecting the alternatives proposed by the White House that call for reducing deficits in part with new revenue from taxes.

McCarthy has insisted personally in his conversations with Biden that tax hikes are off the table.

Republicans also want work requirements on the Medicaid health care program, though the Biden administration has countered that millions of people could lose coverage. The GOP additionally introduced new cuts to food aid by restricting states' ability to waive work requirements in places with high joblessness. But Democrats have said any changes to work requirements for government aid recipients are nonstarters.

GOP lawmakers are also seeking cuts in IRS funding and, by sparing defense and veterans accounts from reductions, would shift the bulk of spending reductions to other federal programs.

The White House has countered by keeping defense and nondefense spending flat next year, which would save $90 billion in the 2024 budget year and $1 trillion over 10 years.

All sides have been eyeing the potential for the package to include a framework to ease federal regulations and speed energy project developments. They are all but certain to claw back some $30 billion in unspent COVID-19 funds now that the pandemic emergency has officially lifted.

For months, Biden had refused to engage in talks over the debt limit, contending that Republicans in Congress were trying to use the borrowing limit vote as leverage to extract administration concessions on other policy priorities.

But with June nearing and Republicans putting their own spending legislation on the table, the White House launched talks on a budget deal that could accompany an increase in the debt limit.

McCarthy faces a hard-right flank that is likely to reject any deal, which has led some Democrats to encourage Biden to resist any compromise with the Republicans and simply raise the debt ceiling on his own to avoid default.

The president, though, said he was ruling out the possibility, for now, of invoking the 14th Amendment as a solution, saying it's an "unresolved" legal question that would become tied up in the courts.