President Joe Biden hosted congressional leaders on Tuesday for a pivotal meeting at the White House as an unofficial June 1 deadline to raise the country's debt limit looms, and while both sides conceded little progress had been made, they agreed to meet again Friday and said their staffs would continue talking in the interim.

Speaking to reporters after the meeting, House Speaker Kevin McCarthy, R-Calif., said that he "didn’t see any new movement," but his Senate counterpart offered a slightly more optimistic tone.

"The United States is not going to default," Senate Minority Leader Mitch McConnell, R-Ky., said after the meeting. "It never has and it never will."

"The United States of America is not gonna default," he said. "We are having a debate here, in conjunction with raising the debt ceiling, as to whether or not dropping $2.6 trillion on the American Congress in the last Congress ... we ought to have at least some restraint."

But, the Kentucky Republican seemed to indicate, there is no chance a clean increase to the debt limit passes the Senate: "Elections have consequences. We now have divided government."

"There are must be an agreement, and the sooner the President and the Speaker can reach an agreement, the sooner we can solve the problem," McConnell said.

"What we have here is, we're running out of time," he warned.

At a press conference at the White House, Biden said he was pleased with McConnell's statement about not defaulting and said he was more optimistic after the meeting than he had been prior. He noted "three of four participants" were "very measured and low-key," but McCarthy occasionally made an "assertion that maybe was a little over the top."

"I trust Kevin will try to do what he says," Biden said. "I don't know how much leeway Kevin McCarthy thinks that he has in light of the fact, and I'm not being a wiseguy when I say this, it took 15 votes to acquire the speakership and apparently he had to make some serious concessions to get it from the most extreme elements of his party. So I just don't know."

At a press conference of his own, McCarthy responded to Biden's remarks by claiming the president was angry during the meeting.

"The House has passed the bill, we raised the debt ceiling. Is it frustrating that the leader of the free world would wait this long and put America in some type of jeopardy? That does make me angry to be honest with you," McCarthy said.

McCarthy, McConnell, House Minority Leader Hakeem Jeffries, D-N.Y., and Senate Majority Leader Chuck Schumer, D-N.Y., were in attendance at Tuesday's summit.

Schumer said that the meeting bore "bad news and good news" – bad, in that McCarthy would not commit to refusing to allow the country to default, but good in that their staffs will begin meeting "as early as tonight, certainly tomorrow" to try and reach an accord on the budget.

"We explicitly asked Speaker McCarthy, would he take default off the table. He refused," Schumer said, adding: "He gave us a plan to take default hostage."

"By not taking default off the table, Speaker McCarthy is greatly endangering America," the New York Democrat lamented.

But, Schumer noted, that staffers will "start sitting down as early as tonight, certainly tomorrow, to see where we can come to agreement on the budget and appropriations process."

He admitted that "there are large differences between the parties," but added: "We can try to come together on those."

McCarthy told reporters that the leaders will meet again on Friday as the debt limit deadline looms, and that their staff will meet in the interim. McCarthy said that he hopes Biden will be "willing to negotiate" in the coming weeks.

The debt limit is the amount of money the U.S. government is authorized to borrow to pay its legal obligations. The $31.4 trillion cap was reached in January, but the Treasury Department has used accounting maneuvers to pay the country’s debts. Treasury Secretary Janet Yellen told Congress last week the U.S. could default on its debts as early as June 1 if lawmakers do not raise or suspend the debt limit.

If Congress fails to act, the U.S. would default on its loans for the first time in its history, resulting in social security, military pay and other checks not going out and the government and Americans being hit with higher interest rates. A U.S. debt default also could roil world markets and potentially trigger a recession, leading to job layoffs, experts say.

Saying he’s concerned government spending has put the nation on a path to economic disaster, McCarthy has demanded spending cuts in exchange for raising the debt limit.

Last month, the Republican-led House passed the Limit, Save, Grow Act, which would lift the debt ceiling by $1.5 trillion into next year while cutting billions in federal spending, capping spending at 1% growth for the next decade and repealing some of Biden’s policy priorities, including multiple aspects of the climate change, social spending and tax reform law known as  the Inflation Reduction Act. 

When asked Tuesday if Biden seemed open to any of his proposed cuts, the California Republican said the president did not.

"I asked him numerous times if three were some places we could find savings," McCarthy said. "He wouldn't give me any."

Biden, meanwhile, has said he thinks it’s dangerous for Republicans to use the potential for default as a bargaining chip and has called on Congress to raise the debt cap without conditions, as it has under other presidents, including when Republicans controlled both chambers of Congress under former President Donald Trump.

“MAGA Republicans are laying out two options for us: 1. Cut veterans’ benefits, Meals on Wheels, education, and health care. 2. Force America to default on its debt,” Biden wrote in a tweet Sunday. “They’re holding the American economy hostage.”

Biden and White House officials have argued that the nation’s debt was amassed over more than 200 years and that it ballooned by nearly $8 trillion during Trump’s four years in office. 

In March, the president proposed a $6.8 trillion budget, which the White House says would cut deficits by nearly $3 trillion over 10 years. Biden’s plan hinges on raising taxes on wealthy Americans and ending subsidies for the oil and gas industry, unpopular measures among conservative lawmakers.

Biden argues the Republicans’ proposed budget would, among other things, put 21 million people at risk of losing Medicaid, result in tens of thousands of federal law enforcement agents and teachers losing their jobs, and make it more difficult for veterans to schedule appointments at Veterans Administration hospitals. 

The White House also has pointed to a Moody’s Analytics report that predicted McCarthy’s plan would slow economic growth and result in 780,000 fewer jobs by the end of 2024 compared to a clean increase to the debt limit.

In Biden’s mind, Tuesday’s meeting is not a debt limit negotiation at all. The president has insisted all along he welcomes dialogue with Republicans on how to reduce the deficit and control the national debt if the talks are not linked to the debt ceiling. 

Biden said Friday he will on Tuesday “reiterate to congressional leaders that they should do what every other Congress has done — that is pass the debt limit, avoid default.”

Senate Republicans, however, made it clear over the weekend that Biden will not find sympathetic allies with them. 

Forty-three GOP members of the Senate sent a letter to Schumer over the weekend saying they are “united behind the House Republican conference” and vowed not to vote on any bill that raises the debt limit “without substantive spending and budget reforms.”

“Our economy is in free fall due to unsustainable fiscal policies,” the letter said. “This trajectory must be addressed with fiscal reforms.”

McConnell, R-Ky., who signed the letter, has insisted he won’t be involved in negotiations.

Sen. Mike Lee, R-Utah, who the led efforts behind the letter, wrote in a tweet: “We have more than enough votes in the Senate to stop any bill raising the debt ceiling without substantive spending and budgetary reforms.”

Meanwhile, the standoff between Biden and McCarthy is stirring debate about whether the president can invoke the 14th Amendment if Congress doesn’t lift the debt limit. 

Section 4 of the amendment states: “The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned.”

On Tuesday, Biden said his administration had considered the option, but was concerned the untested theory would take too long to play out in the courts.

Yellen told ABC’s “This Week” on Sunday that using the 14th Amendment is among a list of “not good options.”

“There is no way to protect our financial system and our economy other than Congress doing its job and raising the debt ceiling and enabling us to pay our bills,” Yellen said. “And we should not get to the point where we need to consider whether the president can go on issuing debt. This would be a constitutional crisis.”

A Washington Post-ABC News poll Friday found that 39% of Americans would blame Republicans if the government goes into default, 36% would blame Biden, and 16% would blame both equally. The opinions fell sharply along party lines. 

Fifty-eight percent of those polled, however, said they think the debt limit and federal spending should be handled as separate issues.