Councils in England have said they are facing a £5.8bn shortfall over the next two years.
The Local Government Association (LGA) has predicted a widening funding gap as the cost of elderly care takes up a growing share of council budgets.
And it said there was now a "once in a generation" chance to steer the social care system "away from financial ruin".
Local Government Minister Brandon Lewis said the LGA claims were "doom laden and alarmist".
BBC local government correspondent Mike Sergeant said councils had "predicted multi-billion pound shortfalls before" and had so far managed to "balance their budgets".
He said this had been done by making cost savings, but there had been some impact on services.
But he said this warning was perhaps the "strongest ever" from LGA chair Sir Merrick Cockell, who said council finances were "on a knife edge".
Sir Merrick also said the next year would be a "make or break moment for adult social care, local services and the NHS".
He also criticised what he called a "vicious cycle of overspending on a broken system", calling instead for the NHS, councils and the government to provide a better, joined-up service for older people.
"Failure to get this right would be catastrophic," Sir Merrick added.
Cuts in government grants have hit council budgets, and the pay of many public sector workers has been affected.
Members of several major unions - including council workers, school support staff and teachers - have voted to strike on 10 July.
Mr Lewis said the LGA's claims lacked 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," he said.
"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 £2bn a year of council tax left uncollected, the £2bn ignored or lost from fraud, the £2.4bn of surplus properties left dormant and the £19bn piled-up in reserves."