Local authorities in England will need to make huge savings before next April, equivalent to 12.5% of their total budgets, according to a new report.
They face a funding gap of £5.8 billion between March 2014 and the end of 2015/16, analysis by the Local Government Association (LGA) found.
The deficit will be caused by a combination of reduced government funding and rising demand on services, in particular from growing numbers of elderly people, it said.
The funding gap in adult social care alone already amounts to £1.9 billion by 2015/16 - based on council adult social care budgets in 2013/14.
The organisation said that, in spite of cuts, local authorities will continue to try to protect spending on adult social care next year as much as possible, which could be at the expense of popular services like buses, libraries and leisure centres.
Next April will mark a critical point for adult social care with the pooling of £5.4 billion from councils and the health service, the LGA said.
The Better Care Fund will aim to improve care for older people and reduce financial pressure on councils and the health system through stopping lengthy waits for discharge from hospitals and avoiding unnecessary admissions to care homes.
LGA chairman Sir Merrick Cockell said: "In recent years, local government has worked tirelessly to save billions while protecting services for those who need them most.
"But the scale of the challenge facing local authorities next year is stark. Council finances are on a knife-edge and the old way of doing things - including the way we care for our elderly population - just won't work any more.
"Next year will be a make or break moment for adult social care, for local services provided by councils and for the NHS.
"The introduction of the Better Care Fund next year is a once-in-a-generation opportunity to both improve the quality of life for people in their older years and steer England's social care system away from the road to financial ruin. The stakes have never been higher.
"We all know that we must do better by our elderly population. Too many older people are being let down by a system which leaves them languishing in hospital beds while they wait for an alternative, or consigned to residential care because we lack the capacity to help them live independently.
"The joined-up approach between councils and the health service will provide better support for less money, by cutting out the cost of failure.
"It will only be through a determined effort from councils, the health service and government working together that we can end the vicious cycle of over-spending on a broken system. Failure to get this right would be catastrophic for an entire generation who rely upon care and the NHS."
Local Government Minister Brandon Lewis said: "The LGA's doom-laden and alarmist claims lack credibility. Councils are balancing their books each year and, as the LGA's own research shows, the public now thinks they are delivering better services than before.
"All the main political parties now agree that public spending is going to remain constrained well into the future. Councils account for a quarter of all public spending so they must continue to play their part reducing the deficit. This means councils must all make that extra effort to spend taxpayers' hard-earned cash ever more wisely.
"There is significant scope for councils to make sensible savings and cut waste by tackling the £2 billion a year of council tax left uncollected, the £2 billion ignored or lost from fraud, the £2.4 billion of surplus properties left dormant and the £19 billion piled-up in reserves."