The Yorkshire Post has been told by council chief executives across the region that they will struggle to meet their legal obligation to balance their books if no more government support arrives in the coming months.
They have already discussed the prospect of many of the 22 local authorities in the Yorkshire and the Humber region making a choreographed joint declaration that they have run out of money.
Issuing so-called Section 114 notices en masse, following the example of crisis-hit Northamptonshire County Council in 2018, would mean the authorities would have to impose severe spending restrictions.
Only the services councils are legally obliged to provide would remain intact, with spending on services like parks, museums and economic development halted or dramatically pared back.
The plan, described by one chief executive as "pressing the nuclear button", is a response to the mounting deficits faced by town halls. Lockdown measures to tackle Covid-19 have resulted in a dramatic loss of income while costs have risen sharply in areas such as social care.
The £3.2bn in crisis funds handed out to towns halls across the country by the Government in recent weeks is seen as being nowhere near enough, with the impact on Yorkshire's councils alone thought to exceed £600m.
Council leaders are urging Chancellor Rishi Sunak to provide long-term funding rather than one-off bailouts so that they can be in a position to help communities recover in the months after the pandemic.
Bradford council chief executive Kersten England said: "Within a year, when we will be dealing with the deep impact of all of this, whether we're in recession or heading for depression, some of what we do to mitigate the worst impacts will be critical.
"And we need to be able to play that part, and having a lack of certainty now to plan properly for that medium to long term is going to prevent us responding as effectively as we might."
Her Scarborough council counterpart Mike Greene said issuing a Section 114 notice "would be the last port of call" once all other options were exhausted.
He said: "We are all looking at that and it's not something that any of us would have expected in our careers to be honest. But ultimately, we've got to continue delivering the services.
"We're providing vital services for people but there will be a very real cost to it and that will come very quickly. Autumn is going to be the crunch point in that respect."
Leeds City Council leader Judith Blake, who chairs the board representing Yorkshire council leaders, said it was "really important that we all stick together and recognise the incredible pressure that local authorities are under and really getting across just how important the work we're doing is".
She said: "It's incredible work that is being done in very very difficult circumstances and I'm sure the Government wouldn't want to reward that commitment and dedication with putting the future of those services at risk."
This week, Communities Secretary Robert Jenrick told the Number 10 press briefing that councils are currently getting more money from the Government for their Covid-19 response than they say they need
A spokesman for the Ministry of Housing, Communities and Local Government said: "Council workers are the unsung heroes as we tackle this pandemic and by providing councils with over £3.2 billion in the fairest way possible we’re working with them to tackle the immediate pressures they have told us they’re facing.
“The 22 councils in the Yorkshire and the Humber region will receive £313.2m of this to deal with the pressures of coronavirus, while their core spending power rose by £268.4m this financial year even before additional emergency funding was announced.
“The Government will continue to work closely with councils as the pandemic progresses."
To read the full special report pick up a copy of this weekend's edition of The Yorkshire Post.