The talks were to take place between President Barack Obama, Vice-President Joe Biden and leaders of the Senate and House of Representatives.
The US government shutdown, also a result of the political deadlock, has now entered its third week.
Officials warn of economic calamity should the US default on its debt.
In a statement, the White House said Monday afternoon’s meeting had been postponed to “allow leaders in the Senate time to continue making important progress towards a solution that raises the debt limit and reopens the government”.
It is unclear when it will be rescheduled.
President Barack Obama sounded his own warning as he toured a soup kitchen for the poor in Washington D.C. earlier on Monday.
“This week if we don’t start making some real progress, both the House and the Senate – and if Republicans aren’t willing to set aside their partisan concerns in order to do what’s right for the country – we stand a good chance of defaulting,” he said.
“And defaulting would have a potentially devastating effect on our economy.”
Barack Obama said he saw “some progress” in the talks, ahead of Thursday’s deadline for the US to raise its $16.7 trillion borrowing limit or risk default on its debt.
Expected to attend the White House meeting were Senate Democratic Majority Leader Harry Reid, Senate Republican Leader Mitch McConnell, Republican House Speaker John Boehner and House Democratic Minority Leader Nancy Pelosi.
On Monday, Harry Reid told the Senate he was “very optimistic we will reach an agreement”. Mr McConnell also expressed optimism, following what he described as “a couple of very useful discussions” with the Democratic leader.
Republican Senator Susan Collins acknowledged the Senate did not have a finished agreement, but said senators were “making very good progress”.
A separate bipartisan group led by Susan Collins also met for several hours earlier in the day to discuss possible solutions, the Associated Press news agency reported.
Congressional Democrats are now said to be using the looming debt ceiling deadline as leverage to push back against previously enacted cuts to the US government budget.
Those deep military and domestic spending cuts, known as the “sequester”, went into effect in January 2013 after Democrats and Republicans failed to reach a budget compromise.
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