Debt–limit talks shifted into an encouraging new phase Tuesday as President Joe Biden and House Speaker Kevin McCarthynamed top emissaries to negotiate a deal to avert an unprecedented national default. Biden cut short an upcoming overseas trip in hopes of closing an agreement before a June 1 deadline.

The fresh set of negotiators means discussions are now largely narrowed to what the White House and McCarthy will accept in order to allow lawmakers to raise the debt limit in the coming days. The speaker said after a meeting with Biden and congressional leaders that a deal was “possible” by week’s end, even as — in McCarthy’s view — the two sides remained far apart for the moment.

Biden was publicly upbeat after a roughly hour–long meeting in the Oval Office, despite having to cancel the Australia and Papua New Guinea portions of his overseas trip that begins Wednesday. Biden will participate in a Group of Seven summitin Hiroshima, Japan, but then return to Washington on Sunday.

“There’s still work to do,” Biden said. “But I made it clear to the speaker and others that we’ll speak regularly over the next several days and staff’s going to continue meeting daily to make sure we do not default.”

Senior White House officials, as well as top aides to the four congressional leaders — McCarthy, Senate Majority Leader Chuck Schumer, D–N.Y., Senate Minority Leader Mitch McConnell, R–Ky., and House Minority Leader Hakeem Jeffries, D–N.Y. — have been meeting daily.

But now, Steve Ricchetti, counselor to the president, Office of Management and Budget Director Shalanda Young and legislative affairs director Louisa Terrell will take the lead in negotiations for the Democratic side, while Rep. Garret Graves, R–La., a key McCarthy ally who has been a point person for the speaker on debt and budget issues, will represent Republicans.

“Now we have a format, a structure,” McCarthy said as he returned to the Capitol.

Negotiators are racing to beat a deadline of June 1, which is when the Treasury Department has said the U.S. could begin defaulting on its debts for the first time in history and risk a financial catastrophe. The revised itinerary of Biden’s upcoming trip showed the urgency of the talks,

White House officials sought to soften the impact of the trip cancellations. National Security Council spokesman John Kirby noted that Biden will already have met with some of the leaders of the “Quad” — the purpose of the Australia leg of the visit — while in Japan, and the president is inviting Australian Prime Minister Anthony Albanese for an official state visit in Washington.

Still, Kirby added: “We wouldn’t even be having this discussion about the effect of the debt ceiling debate on the trip if Congress would do its job, raise the debt ceiling the way they’ve always done.”

Even as the Democratic president and the Republican speaker box around the politics of the issue — with Biden insisting he’s not negotiating over the debt ceiling and McCarthy working to extract spending cuts with the backdrop of a potential default — various areas of possible agreement appeared to be emerging.