The Chancellor will outline his update on Government plans for the economy during the Autumn Statement on December 4.
But the Local Government Association (LGA) has said the country needs a period of a period of financial stability to allow councils to plan for the largest, most sustained cuts to the funding for local services since the war.
In a statement released yesterday the LGA said that as a result of delivering £10 billion of real-terms savings in the three years from 2011/12 and a further £10bn over the next two years at a time of growing demands for social care, "councils in many areas will not have enough money to meet all their statutory responsibilities."
It said that the amount available for non-social care, such as parks, was predicted to shrink by 66 per cent by the end of the decade.
The LGA, which represents 373 councils in England and Wales, believes the Treasury has a binding obligation to deliver the grant funding it has committed to provide to local government in 2014/15 and 2015/16 and warns that a failure to meet the existing commitment will push even more councils beyond breaking point.
It says the cuts already scheduled for those two years amount to 21 per cent of total funding and will bring to 43 per cent the total cuts to local authority funding announced by this Government.
LGA chairman Sir Merrick Cockell said: "The next two years are make or break for many councils and the Chancellor has it in his power to either deliver a stable environment in which they can plan for the unprecedented challenges ahead, or he can deliver uncertainty and risk which will put even more stress on vital local services and push councils toward failure.
"This Government is testing the resilience of councils to breaking point and in many areas the cracks are starting to show. 2015/16 is shaping up as the crunch year and we expect some councils to be placed in a position where they do not have the money they need to meet their statutory obligations.
"Councils need a period of stability and consistency so they can plan for the unprecedented challenges which lie ahead."