Democratic and Republican leaders walked out of the Oval Office Tuesday afternoon announcing a new structure for the debt-ceiling talks but apparently little closer to a deal as they seek to avoid potential default as early as June.

"We've got a lot of work to do in a short amount of time,” House Speaker Kevin McCarthy (R-CA) told reporters at the White House after the meeting, the second between President Biden and other leaders this month.

But leaders did announce one positive development: The discussions will now be handled by a smaller contingent of White House officials and McCarthy allies instead of a larger, more unwieldy group of negotiators.

White House Counselor Steve Ricchetti, OMB Director Shalanda Young and and White House Legislative Affairs director Louisa Terrell will lead the discussions for Biden. McCarthy's staff and Rep. Garret Graves (R-LA) will lead from the GOP side.

McCarthy added Tuesday he hopes those talks begin today and that, in spite of little apparent progress on issues, "it's possible to get a deal by the end of the week." The speaker has previously said the framework of a deal is needed within days to get a bill written and through Congress before June 1.

“The bottom line is that we all came to an agreement” to continue talks under the new structure, added Senate Majority Leader Chuck Schumer (D-NY), who said the meeting was much more cordial than last week. Vice President Kamala Harris, Senate Minority Leader Mitch McConnell (R-KY) and House Minority Leader Hakeem Jeffries (D-NY) also joined the meeting.

The White House also announced plans Tuesday to shorten an overseas trip to focus on the talks in the weeks ahead. Biden had been scheduled to stop in Japan, Papua New Guinea, and Australia but the latter two stops will be scrapped.

Biden still plans to travel to Hiroshima for a G-7 meeting, leaving tomorrow, but then would return Sunday for more talks. Biden promised to check in on the talks by phone during his upcoming travel.

In a statement, the White House called today's gathering a "productive and direct meeting" and indicated that the aim now is for a bipartisan budget agreement where it is likely that "neither side will get everything it wants."

Tuesday's meeting among the leaders came after a week of negotiations among aides resulted in tentative progress on issues like permitting reform and work requirements for social programs. Still, the lack of concrete progress on issues Tuesday is likely to do little to quell growing fears that progress towards a deal isn’t coming quickly enough in the face of a fast-approaching June 1 deadline.

Business worries of an ‘economic and financial catastrophe’

Tuesday’s meeting came after a day where markets stumbled somewhat, partly in response to debt-ceiling fears alongside other issues like fresh economic data and weak retail earnings.

In spite of the clear risks to the economy, markets have largely been sanguine about the ongoing gridlock, looking towards historical precedents like the 2011 standoff that ended at the last minute with a deal.

But Janet Yellen and others warn it could be different this time. The Treasury Secretary sounded the alarm once again Tuesday morning about what she calls the “economic and financial catastrophe” that could accompany failure in the weeks ahead.

“It is very conceivable that we’d see a number of financial markets break – with worldwide panic triggering margin calls, runs, and fire sales,” she said Monday morning at a summit hosted by the Independent Community Bankers of America.

And in a Yahoo Finance Live appearance, Sen. Jack Reed (D-RI) called for business leaders to apply pressure, arguing that when they “privately weigh in, that could make a real difference.”

But help for Democrats doesn’t appear to be forthcoming from at least from one powerful quarter. On Tuesday morning, JPMorgan Chase CEO Jamie Dimon pushed back on the notion of pressuring Republicans to relent while speaking during his bank's annual shareholder meeting.

"I don't think it's our job to put pressure on Republicans in Congress...I think that politicians should resolve this,” Dimon said.

Dimon has previously announced a ‘war room’ to deal with possible default.

Democratic fears of ‘a pretty dangerous direction’ for talks

Tuesday’s meeting also came in the context of increasing pressure from Biden’s left flank after days of the negotiations where the president publicly put more and more items on the table.

The political pressure is likely to only increase following Tuesday's White House statement that acknowledged the goal now is a "bipartisan budget agreement" to cover both default and budget issues after months of saying negotiations over the debt ceiling are a non-starter.

“The negotiations are headed in a pretty dangerous direction if the administration is ready to potentially agree to sizable spending cuts and other draconian poverty measures like enhanced work requirements,” said Lindsay Owens, the executive director of the progressive group Groundwork Collaborative, in an interview Tuesday before the talks.

Biden in recent days has seemed to open the door to negotiation on the controversial topic of work requirements for social programs and also signaled a willingness to talk about other issues like spending cuts and taking back money appropriated by Congress for COVID relief bills.

In a Yahoo Finance Live interview Tuesday, Sen. Elizabeth Warren called the Republican push for increased work requirements “fundamentally wrong” and claimed Republicans were looking to toss people on the street.

“If those Republicans are really serious about reducing the national debt, then let’s start by raising more revenues,” she added. Warren also told reporters Tuesday she could vote against a final deal if it includes things like work requirements.

But overall, McCarthy said Tuesday that while he was "not more optimistic" about the overall chances of reaching a deal, he said the new negotiating structure was a positive development that has worked to achieve progress in the past.

This post has been updated.

Ben Werschkul is Washington correspondent for Yahoo Finance. David Hollerith contributed reporting.

Click here for politics news related to business and money

Read the latest financial and business news from Yahoo Finance