Congressional leaders on Tuesday said President Biden agreed to have the White House negotiate the debt ceiling directly with House Speaker Kevin McCarthy's office.

Why it matters: Biden is acceding to a key demand by Republican lawmakers – for the White House to acknowledge the House GOP majority's leverage in the process and act accordingly.

What they're saying: McCarthy (R-Calif.) and other congressional leaders emerged from an hour-long White House meeting telling reporters progress was made.

• "I think we set the stage to carry on further conversations ... We've got a lot of work to do in a short amount of time," McCarthy said.
• The speaker said Biden "changed the scope of who's all negotiating" by agreeing to appoint White House officials to negotiate directly with his team.
• Senate Minority Leader Mitch McConnell (R-Ky.) said Biden and McCarthy are "the keys to the deal," adding, "I'm prepared to try to deliver as much as I can for whatever the speaker and the president can agree to."

The context: The meeting comes as Treasury Secretary Janet Yellen reiterating her warning that the U.S. could run out of money to pay its debts as soon as June 1.

• Biden previously met with the four congressional leaders last week, which kicked off staff-level negotiations that have been going on in the interim.
• Republicans have argued that Biden needs to negotiate directly with McCarthy, whose support is necessary for any bill to pass the House.
• "It sounds like there might be too many cooks in the kitchen," Rep. Andrew Garbarino (R-N.Y.) told Axios after a House GOP leadership meeting on Monday. "Maybe it should just be the president discussing this with McCarthy."

The details: Biden is tapping White House counselor Steve Ricchetti and Office of Management, Budget Director Shalanda Young and White House legislative affairs director Louisa Terrell as his point people, according to a White House official.

• Rep. Garrett Graves (R-La.), a McCarthy ally, will represent the House GOP along with members of the speaker’s staff, McCarthy said.
• "The President directed staff to continue to meet daily on outstanding issues," the White House said in a readout of the meeting. "He said that he would like to check in with leaders later this week by phone, and meet with them upon his return from overseas."
• Biden is shortening his trip to Asia after the G7 summit, the White House announced Tuesday.

What we're watching: McCarthy said "it is possible to get a deal by the end of the week."

• Asked how much the bill may raise the debt ceiling, McCarthy said "that's all up for negotiation."