• President Joe Biden will meet with House Speaker Kevin McCarthy on Tuesday afternoon alongside other top congressional leaders to try to come to an agreement on raising the debt limit.
• Staff from both sides have been working daily since the leaders met last week to try to come to a deal before early June, when the federal government could run out of money.
• The leaders left their meeting a week ago with little progress to show.

WASHINGTON — President Joe Biden is set to meet with House Speaker Kevin McCarthy on Tuesday afternoon alongside other top congressional leaders to discuss the debt ceiling, a day before Biden is slated to head to Japan for the Group of Seven summit.

Behind the scenes, staff from both sides have been working daily since the leaders met last week to try to come to a deal before June, when the federal government could run out of money. The leaders left the previous meeting with little progress to show.

"I really think there's a desire on their part, as well as ours, to reach an agreement, and I think we'll be able to do it," Biden told reporters Sunday in Delaware. As to his state of mind, he said, "I remain optimistic because I'm a congenital optimist."

McCarthy sang a different tune, telling NBC News on Monday outside the Capitol, "I still think we're far apart."

"It doesn't seem to me yet that they want a deal," McCarthy said. "It seems like they want to look like they're in a meeting. They're not talking anything serious." 

Biden and McCarthy were slated to meet again Friday with Senate Majority Leader Chuck Schumer, Senate Minority Leader Mitch McConnell and House Minority Leader Hakeem Jeffries, who attended the last meeting, but that was postponed as negotiations continued behind the scenes. Vice President Kamala Harris will also attend this time.

A source familiar with the meetings told NBC News that the delay is a positive development and a sign that talks were "progressing."

The White House has maintained that Biden intends to go to the G-7 summit in Japan later this week, but the president himself has said that could change depending on the debt ceiling talks. After the G-7 trip, Biden was slated to travel to Papua New Guinea before going to Australia for a meeting of the leaders of the "Quad" nations, the U.S., Australia, Japan and India.

McCarthy told reporters it was critical that they reach a deal before this weekend so the bill would have enough time to pass through both chambers of Congress and make it back to the president's desk for signing.

The discussions have high stakes: Defaulting on sovereign debt would wreak havoc on the economy and roil global markets. A default on Treasury bonds could throw the U.S. economy into a tailspin. The last time congressional Republicans threatened a default in 2011, Standard & Poor's downgraded the U.S. credit rating for the first time ever to AA+ from AAA.

Lifting the debt ceiling is necessary for the government to cover spending commitments already approved by Congress and the president and prevent default. Doing so does not authorize new spending. But House Republicans have said they will not lift the limit if Biden and lawmakers do not agree to future spending cuts.

The Treasury Department has taken extraordinary steps to keep paying the government's bills, and expects to be able to avoid a first-ever default at least until early June. Treasury Secretary Janet Yellen warned last week failure to hike the debt ceiling would cause an "economic catastrophe."

If the U.S. were to default, gross domestic product would drop 4% and more than 7 million workers would lose their jobs, Moody's Analytics recently projected. Even a brief default would lead to the loss of 2 million jobs, according to the data.