Also known as the debt limit, this is a law that limits the total amount of money the government can borrow to pay its bills.

This includes paying for federal employees, the military, Social Security and Medicare, as well as interest on the national debt and tax refunds.

Every so often US Congress votes to raise or suspend the ceiling so it can borrow more.

The cap currently stands at roughly $31.4tn (£25.2tn). That limit was breached in January, but the Treasury Department used “extraordinary measures” to provide the government with more cash while it figured out what to do.

Usually it’s a formality for Congress to raise the limit as needed but this time it can’t seem to agree on the terms.

Treasury Secretary Janet Yellen has warned that without more borrowing, the US will not have enough money to meet all of its financial obligations as soon as 1 June.

This has never happened before so it is not entirely clear, but it would cause major economic damage.

The government would no longer be able to pay the salaries of federal and military employees, or pensions.

National parks and other agencies would shut down, while companies and charities that count on government funds would be in peril.

Weather forecasts could be affected since so many rely on data from the government-funded National Weather Service.

If the government stops making interest payments on its debt, that would also put the country into default. The US briefly entered default in 1979, which the Treasury blamed on an accidental cheque processing issue, but an intentional default would shock the financial system where more than $500bn in US debt gets traded every day.

Moody’s Analytics predicts that in a prolonged stand-off, stock prices would fall by almost a fifth and the economy would contract more than 4%, leading to the loss of more than seven million jobs.

Over the long term, if investors start to see US debt as risky they will charge the US more to borrow money. And since government borrowing helps determine interest rates more widely, the impact would trickle out to the rest of the economy, making borrowing money for a home or a car more expensive for everyone.

There are debates about whether the government could prioritise interest payments to avoid a debt default. But honouring commitments to the owners of US debt, which include financial firms, pension funds and foreign investors, while retirees and others go unpaid is seen as a difficult one to sell politically.

Last month, Republicans put forward a deal to suspend the debt limit by $1.5tn or until 31 March.

In exchange, they would keep spending for key agencies at 2022 levels during the next financial year- and limit growth to 1% annually over the next decade – moves that could lead to $4.8tn in savings.

The proposal would repeal key priorities of the Biden administration, such as student loan forgiveness and tax incentives for electric vehicles.

The White House has said the deal forces “middle class and working families to bear the burden of tax cuts for the wealthiest” and has “no chance” of becoming law.

Many analysts expect a short-term extension to give Congress more time to reach a deal. Others are floating more radical ideas, like minting a $1tn coin to pay debt or urging the president to declare that respecting government debt is a constitutional requirement.

In 2011, the last time the US was seen as at serious risk of a default, talks went down to the wire, before a compromise deal including $900bn in spending cuts over 10 years was announced hours before the deadline.

But even delays have consequences.

The 2011 stand-off prompted a downgrade in the US credit rating, sent the stock market plunging – and is estimated to have cost the public at least $1.3bn in higher borrowing costs that year alone.

The debt limit debate highlights one of the fundamental ideological differences between the two major US political parties.

The Republicans view government spending sceptically. To them, rising national debt is evidence of out-of-control government.

While debt-limit brinksmanship is a relatively new strategy for the party, many Republicans believe it is necessary because the nation’s current course will ultimately lead to economic and social ruin.

Democrats, on the whole, view national government power as a force for good – a means to improve American lives and right historical wrongs.

They see raising the debt limit when necessary as housekeeping necessary to maintain the operation of the government.

The national debt, in their view, is simply a means to fund legislative programmes that have already been discussed and approved.