President Joe Biden and House Speaker Kevin McCarthy met in the Oval Office for more than hour Wednesday, and afterward McCarthy called it a "good first meeting," suggesting the two men might find a compromise over spending.
At the same time, he said there were "no agreements" and "no promises" made.
The highly anticipated meeting, the first the two men have held since McCarthy narrowly won the speakership last month, comes amid an ongoing standoff over the national debt limit.
"I think, at the of the day, we can find common ground, I really do," McCarthy told reporters in the White House driveway.
A few minutes later, the White House released its take on the meeting, saying the two men had a "frank and straightforward dialogue" and that the conversation would continue.
"They covered a range of issues and President Biden underscored that he is eager to continue working across the aisle in good faith," the statement said.
The White House said that Biden "made clear" that they cannot allow the U.S. to default and that this obligation is "not negotiable or conditional," adding that Biden "welcomes a separate discussion" on reducing the deficit.
The president had told reporters Monday that his message for McCarthy would be "show me your budget," showing specific cuts he's proposing in exchange for Republican support to lift the debt ceiling -- and avoid a catastrophic default.
Asked Wednesday by ABC News Senior White House Correspondent Mary Bruce when he would share the "big plan" he has promised, McCarthy responded, "I think the president and I have talked about a lot of different ideas and we'll work to see if we can come to an agreement."
Pressed further, McCarthy fired back, "I know you all have a job to do but I don't think we'll come to an agreement if I negotiate with you."
The White House has repeatedly said it would not negotiate with Republicans -- that the stakes for the U.S. economy were too high, and that the limit had been raised 74 times before, including with Republican support under then-President Donald Trump.
But on Tuesday, the president suggested he was open to talking. Asked if he would negotiate with the speaker during Wednesday's meeting, Biden responded simply, "Show me his budget."
The president has long cast himself as a dealmaker, eager to sit down with Republicans to reach bipartisan agreements. At a fundraiser in New York on Tuesday, Biden referred to McCarthy as "a decent man."
But he has also lambasted congressional Republicans as "extreme" and said McCarthy had given in to that faction to take control.
"Look at what he had to do," the president said Tuesday. "He had to make commitments that were just absolutely off the wall for a speaker of the House to make in terms of being able to become a leader."
Responding to Biden's comments at the fundraiser, McCarthy said, "apparently he doesn't understand."
"I'm looking forward to sitting down with the president negotiating for the American public -- the people of America -- on how we can find savings," McCarthy said.
When asked if he planned to make Biden a specific offer, McCarthy said, "I think we're gonna sit down and negotiate."
That public posturing was only the latest salvo launched between the two men.
Earlier Tuesday, McCarthy told reporters that he was "willing to sit down" with Biden "and finally get this done long before the debt limit hits its point that we have to get something done."
"Because why would you put the economics of America in jeopardy?" he said. "Why would you play political games?"
McCarthy has noted he and Biden had "met many times prior to him being president," although "not as often as being president."
He said Tuesday the White House should "say they're willing to negotiate, because the only irresponsible way is to play a political game and say, we're not going to talk about it. It sounds pretty childish to me."
Earlier in the day, top White House officials wrote in a memo that Biden planned to pose two questions to McCarthy during the meeting.
The president is expected to ask McCarthy if he will "commit to the bedrock principle that the United States will never default on its financial obligations" and whether he agrees with "former presidents, including Presidents Trump and Reagan, that it is critical to avoid debt limit brinksmanship," according to the memo, which was first obtained by ABC News.
The authors of the memo -- the president's top economic adviser, Brian Deese, and the director of the White House budget office, Shalanda Young – noted Biden planned to release a budget on March 9. They challenged McCarthy to do the same.
"It is essential," they wrote, "that Speaker McCarthy likewise commit to releasing a budget, so that the American people can see how House Republicans plan to reduce the deficit – whether through Social Security cuts; cuts to Medicare, Medicaid, and Affordable Care Act (ACA) health coverage; and/or cuts to research, education, and public safety – as well as how much their Budget will add to the deficit with tax cuts for the wealthiest Americans and large corporations, as in their first bill this year."
In response, McCarthy wrote in a statement Tuesday: "Mr. President: I received your staff's memo. I'm not interested in political games. I'm coming to negotiate for the American people."
Republicans in the House have insisted on deep spending cuts in exchange for their cooperation on raising the debt ceiling.
The Republican Study Committee, which represents the largest group of Republicans in the House, previously called for revisions to Social Security and Medicare, including raising the age for Medicare to 67 and Social Security to the age of 70 for younger workers.
But McCarthy recently said any cuts to Social Security and Medicare would be "off the table."
McCarthy pointed to the "Commitment to America" plan presented by Republicans before the midterms, which he said "strengthens" Medicare and Social Security. The White House has accused McCarthy of being "evasive" on his plan for government spending.
Pressed on what he meant by "strengthen" and whether he would seek to raise the retirement age -- McCarthy said: "No, no, no. What I'm talking about Social Security, Medicare, you keep that to the side."
"I want to find a reasonable and a responsible way that we can lift the debt ceiling but take control of this runaway spending," McCarthy said.
Senate Minority Leader Mitch McConnell has expressed support for McCarthy. "We're all behind Kevin," he said Tuesday. "Wishing him well in the negotiations."
Meanwhile, the White House has repeatedly said Biden will not negotiate or compromise by tying a debt limit increase to spending cuts, with the administration pointing to the bipartisan history of the ceiling being increased by both parties over the years.
"Attempts to exploit the debt ceiling as leverage will not work," White House press secretary Karine Jean-Pierre told reporters last month. "There will be no hostage taking."
Earlier this month, McCarthy made it clear he was holding firm.
"For the president to say he wouldn't even negotiate -- that's irresponsible. We're going to be responsible. We're going to be sensible, and we're going to get this done together. So the longer he waits, the more he puts the fiscal jeopardy of America up for grabs," McCarthy told ABC News Senior Congressional Correspondent Rachel Scott last month. "We should sit down and get this done and stop playing politics," he added.
The debt limit doesn't allow government spending on new programs -- instead it allows the U.S. to borrow any money it needs to pay for the nation's existing bills.
The federal government hit the current debt ceiling, about $31.4 trillion earlier this month prompting the Treasury Department to step in with "extraordinary measures" which will allow the nation to avert a catastrophic default until June.
"President Biden will ask Speaker McCarthy to publicly assure the American people and the rest of the world that the United States will, as always, honor all of its financial obligations," the memo stated.
ABC News' Lauren Peller and Allison Pecorin contributed to this report.