Will there be enough time to get a deal through?
By Anthony Zurcher and Natalie ShermanBBC News, Washington and New York
Getty ImagesUS President Joe Biden and Republican leader Kevin McCarthy have called their latest talks on the debt ceiling productive but no deal has yet been reached.
Any agreement will have to pass through Congress. With just nine full days till the estimated debt-limit deadline of 1 June, hitting that date is looking increasingly difficult.
The US Senate is currently out of session and the House of Representatives has a planned recess this weekend for the Memorial Day holiday on Monday 29 May.
Congressional leaders could call the chambers back, but simply getting enough legislators in town to vote will be a logistical challenge.
Of the nine days left, only six are working days. House Speaker Mr McCarthy estimated that it would take about a week for Congress to raise the debt limit smoothly.
He has promised to allow at least 72 hours for members of his chamber to review the text of any agreement prior to passage. That means the deal would in theory need to come by early Friday 26 May at the latest. He could press ahead and give them less time, but it would be at the risk of angering those in his party who want to go over the text with a microscope.
The Senate will also have to approve the legislation - and in that chamber, even one recalcitrant legislator can delay a vote for days. A senator with an eye for publicity or an agenda to advance who is willing to risk the wrath of his colleagues could put the entire process at risk.
Once the full Congress approves a deal, staff will have to scramble to go over technical details to prepare the bill for Mr Biden's signature. The process can typically take days or even weeks.
With time running short, however, a team of congressional staff working in concert could have legislation ready for the president in hours. But rushing it comes at the risk of introducing errors or loopholes that could cause problems down the road.
With some money coming in each day, some analysts say the government may be able to squeeze by past Janet Yellen's 1 June deadline until 15 June, when it will get an influx of funds from companies paying quarterly tax bills.
Analysts say the Treasury could pay its bills more slowly to try to manage its money. The first major debt payment is also not due until 15 June, which reduces the risk that the US could be forced to default on its debt.
But the US will likely need to find roughly $290bn (£234bn) in cash to make it that far, according to financial forecasters Oxford Economics.
And stretching the deadline beyond 1 June will be "hovering in a very dangerous zone", said analysts at RBC Capital Markets, which estimate the Treasury's resources will stand at around just $40-60bn for the first two weeks of June.
"This is extremely low," they note. "Several days of heavier-than-expected net outflows, or unexpected changes in intragovernmental debt, could exhaust that small buffer quickly and unexpectedly."
Many investors are betting that Treasury would choose to make some debt payments and miss other obligations, as has been debated during prior debt ceiling stand-offs.
But Ms Yellen has previously called that sort of prioritisation "default by another name".
If push comes to shove, Congress could always try to pass a short-term increase in the debt limit in order to buy White House and Republican negotiators more time to reach an agreement.
Some suggestions have been to move the deadline into at least July or even August. But for now, neither side seems interested in such a move unless it is very clear that a deal is near at hand.
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