Talks between the White House and the Senate’s top Republican and Democrat broke up Tuesday with no progress on raising the country’s debt ceiling, an impasse that threatens a financial crisis if left unresolved.

The Senate and House have 12 joint working days before Sept. 29, when the Treasury Department says it would no longer be able to pay all of the government’s bills unless Congress acts. A default would likely set off a major disruption to the world financial system, with a stock market crash and surging interest rates that could send the economy into a recession.

Treasury Secretary Steven Mnuchin has urged Congress for months to raise the debt limit, but the White House has lacked a unified message and run into resistance on Capitol Hill, where Democrats and Republicans are at odds on key tax and spending issues.

Mnuchin met Tuesday morning with Senate Majority Leader Mitch McConnell (R-Ky.) and Senate Minority Leader Charles E. Schumer (D-N.Y.), searching for ways to raise the debt ceiling, but the gathering ended without any progress — or even a clear sense of what the lawmakers need to deliver votes to raise the limit, according to three people briefed on the meeting who insisted on anonymity to speak candidly about the private discussions.

Several hours after the meeting, White House spokeswoman Sarah Huckabee Sanders implored Congress to act, illustrating how serious the Trump administration now believes this issue to be.

“To ensure that we have robust economic growth and promote fiscal discipline, the Trump administration believes it’s important to raise the debt ceiling as soon as possible," she said at her daily press briefing. "Over the past two decades, members of Congress and presidents from both parties have raised debt ceiling 15 time and we look forward to working with Congress to ensure the full faith and credit of the United States government.”

But lawmakers so far have shown little sign of engaging. The House of Representatives has already left town and will not return until after Labor Day.

The U.S. government spends more money than it brings in through revenue, creating an annual deficit. The Treasury Department borrows money to cover that gap by issuing debt, and it has always paid back the bondholders on time. According to one measurement, the government now has close to $20 trillion in debt.

Congress has established a cap on the amount of money the government can borrow, and Mnuchin has told Congress that this cap must be raised by Sept. 29 to ensure that the government can continue paying all of its bills.

Republicans often resist efforts to raise the debt ceiling, making GOP leaders rely on Democrats to help them get enough votes to pass the bill. But substantive talks on how to raise the debt ceiling have not yet begun, and the breakdown at the Mnuchin meeting on Tuesday suggests a vote on the measure could come down to the wire late next month.

A number of Republicans, and even some within the White House, have suggested that there should be spending cuts that accompany any agreement to raise the debt ceiling, a condition that many Democrats have said they will not accept. Democrats, meanwhile, have also signaled they will not agree to raise the debt ceiling if Republicans plan to then add trillions of dollars in debt through a large tax-cut package.

President Barack Obama's administration and Congress almost failed in their efforts to raise the debt ceiling in 2011, and the uncertainty roiled financial markets. They ultimately agreed to a series of budget caps and other changes in exchange for raising the borrowing limit, but the Obama administration later adopted a position that it would not negotiate any future changes to the debt ceiling.

President Trump's administration has not had to raise the debt ceiling yet, and Trump has ridiculed Republicans in the past for agreeing to lift the borrowing limits when Obama was in office.

-- David Nakamura contributed to this report.