House Speaker Kevin McCarthy suggested a debt-ceiling meeting with President Joe Biden Tuesday didn’t break any new ground but both sides offered glimmers of hope that the looming crisis can still eventually be averted.

After an hour-long meeting in the Oval Office, McCarthy told reporters “I didn’t see any new movement” and that both sides remained at loggerheads over issues like spending cuts.

But he also said staff members would continue to meet and that the leaders would gather again Friday, indicating that talks haven’t broken down.

For his part, Biden called it a "productive meeting" during his own press conference Tuesday evening but also noted that the meeting was sometimes tense and claimed McCarthy occasionally made assertions that were “over the top.”

Biden also announced that staff meetings would begin tonight and will continue every day between now and Friday.

But the president also acknowledged that deep policy differences remain, especially over spending, and that Republicans aren’t being forthright about the depth of their cuts. “I’m not sure they know exactly what they are proposing.”

Other lawmakers present at the meeting offered a mix of positive and negative signs. Senate Majority Leader Chuck Schumer (D-NY) speaking alongside House Democratic Leader Hakeem Jeffries (D-NY), said "there are probably some places where we can agree."

Senate Minority Leader Mitch McConnell (R-KY), speaking alongside McCarthy after the meeting, also offered some hope. He said “the United States is not going to default: It never has and it never will.”

The highly-anticipated Oval Office gathering came more than 3 months after the two leaders last sat down to discuss fiscal issues and just days after Treasury Secretary Janet Yellen announced that a US default could come as early as June 1.

The meeting began with a smile when President Biden wryly told reporters “we’re going to get started, we're going to solve all the world’s problems.” But the meeting only lasted about an hour and clearly didn't yield any sort of breakthrough.

Pressure from business groups

What observers will be closely watching as the talks progress in the days ahead are any signs that Republicans and Democrats are moving away from what are currently irreconcilable positions.

The meeting also comes amid increasing fears from Wall Street that the standoff will at a minimum put downward pressure on stocks through the rest of the month as Washington again flirts with a default.

On Tuesday, stocks closed lower Tuesday as investors waited for developments from Washington about whether the talks would lessen the likelihood of a default within weeks.

Business groups have also been weighing in ahead of the meeting with Neil Bradley of the U.S. Chamber of Commerce calling for a swift agreement and adding that the twin issues of spending caps and energy permitting reform are “two areas that are ripe for inclusion.”

Business Roundtable CEO Joshua Bolten reacted to the meeting by welcoming the beginning of bipartisan negotiation saying "the economic consequences of a default, or even the threat of a default, are simply too high."

The White House has also recently emphasized the economic costs of default, with Yellen calling it a recipe for “economic calamity.”

During a Yahoo Finance Live appearance on Tuesday, political strategist Steve Schmidt warned Wall Street observers that the outcome here will be very hard to predict. “There is no rationality in this and that's what's broken about American politics,” he said.

Next steps

Before the leaders reconvene on Friday, President Biden is set to travel Wednesday to New York's Hudson River Valley. There he will give a speech on the debt limit in the district of Rep. Mike Lawler (R-NY), a vulnerable Republican under pressure to break from his party.

One intriguing development Tuesday was when Lawler told the Associated Press he would be appearing alongside Biden during the Wednesday stop. He said the White House had invited him to join and he accepted “maybe to their surprise.”

Another wrinkle sure to complicate the weeks ahead is an overseas trip Biden has planned for later this month that will take him to Japan, Australia, and Papua New Guinea. He is scheduled to return just days before default is on the table on June 1.

On Tuesday, McCarthy also said he opposes the idea of a short-term extension through Sept. 30. He said he thinks the two sides have about two weeks to get to a deal, adding a hope that Biden would continue to negotiate "and not take America to the brink."

This post has been updated with additional developments.

Ben Werschkul is Washington correspondent for Yahoo Finance.

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