Raising the stakes, the Tuesday afternoon session comes as Biden is preparing to depart for the Group of Seven summit in Japan where the U.S. leadership will be on the world stage later this week. The president and House Speaker Kevin McCarthy are trying to strike a budget deal before the U.S. Treasury runs out of cash to keep paying the nation’s bills, which could occur as soon as June 1.

While Biden has remained upbeat that “we’ll be able to do this,” McCarthy is prodding the president to move faster to avert a crisis. The Republican speaker says they need an agreement soon to avoid default. Expectations are low that a deal is that close at hand. Instead, it is more likely that staff talks will continue while the president is overseas.

“I just don’t see the progress happening,” McCarthy told reporters Monday.

But Biden was optimistic, saying over the weekend, “There’s a desire on their part as well as ours to reach an agreement.”

It’s the second time in a week that Biden has met with McCarthy of California and other congressional leaders at the White House. Biden is confronting a politically divided Congress for the first time on the debt ceiling, a test for both the president and McCarthy, the new speaker, as they work to stave off an economic crisis that could come from a federal default. The meeting will also include Senate Majority Leader Chuck Schumer of New York, Senate Republican leader Mitch McConnell of Kentucky and House Democratic leader Hakeem Jeffries of New York.

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 — various areas of possible agreement appear to be emerging.

Talks have been under way at the Capitol for much of the past week, closed-door discussions where White House and congressional staff are discussing what it would take to craft a budget deal that would unlock a separate vote to lift the nation’s borrowing capacity, now set at $31 trillion.

Among the items on the table: clawing back some $30 billion in untapped COVID-19 money, imposing future budget caps, approving permitting reforms to ease energy development and putting bolstered work requirements on recipients of government aid, according to those familiar with the talks.

McCarthy has complained the talks are slow-going, saying he first met with Biden more than 100 days ago and that the president should be more focused on issues at home.

“An American president should focus on the solutions of America,” McCarthy said ahead of Biden’s trip.

But Biden has insisted Republicans must rule out default and consider budget issues separate from the need to raise the nation’s debt limit. The president has said it took McCarthy all this time to put forward his own proposal after Republicans failed to produce their own budget this year.

The debt limit must be lifted, as has been done countless times before, to allow continued borrowing to pay already accrued bills.

Compounding pressure on Washington to strike a deal, Treasury Secretary Janet Yellen said Monday that agency estimates are unchanged on the possible X-date when the U.S. could run out of cash — perhaps as early as June 1.

But Yellen, in a letter to the House and Senate, left some opening for a possible time extension on a national default, stating that “the actual date Treasury exhausts extraordinary measures could be a number of days or weeks later than these estimates.”

She said she would update Congress next week “as more information becomes available.”

Time is dwindling. Congress has just a few days when both the House and Senate are in session to pass legislation.

“It’s time for the principals to get more engaged, get their closers out there,” said Sen. John Thune of South Dakota, the Republican whip. “My impression is that they have too many cooks in the kitchen, too many people in the room and not the right people.”

Details of a potential budget deal remain politically daunting, and it’s not at all clear they go far enough to satisfy McCarthy’s hard-right faction in the House or would be acceptable to a sizable number of Democrats whose votes would almost certainly be needed to secure any final deal.

Republicans led by McCarthy want Biden to accept their proposal to roll back spending, cap future outlays and make other policy changes in the package passed last month by House Republicans. McCarthy says the House is the only chamber that has taken action to raise the debt ceiling. But the House bill is almost certain to fail in the Senate, controlled by Democrats, and Biden has said he would veto it.

Biden did signal over the weekend that he could be open to tougher work requirements for certain government aid programs, which Republicans are proposing as part of the ongoing discussion. He has said he will not accept anything that takes away people’s health care coverage.

An increase in the debt limit would not authorize new federal spending. It would only allow for borrowing to pay for what Congress has already approved.

As June 1 approaches, the nonpartisan Congressional Budget Office has warned of a “significant risk” of default sometime in the first two weeks of next month.

The CBO noted that if the cash flow at the Treasury and the “extraordinary measures” that the department is now using can continue to pay for bills through June 15, the government can probably finance its operations through the end of July. That’s because the expected tax revenues that will come in mid-June and other measures will give the federal government enough cash for at least a few more weeks.