It voiced its fears ahead of the expected local government settlement, one of the last in which central government funding will be included.
The settlement is expected to be announced this or next week.
The LGA urged the government to use the settlement to avoid “a financial breaking point which will threaten the existence of some local services by 2020”.
Central government funding of councils was due to fall by £2.7bn between 2018-20, equivalent to a 54% cut, originally intended to coincide with local government keeping 100% of its business rates income.
But the Local Government Finance Bill, which would have given effect to this, fell once last June’s general election was called and was not reintroduced in the Queen’s Speech.
The policy has not officially been scrapped but is not now expected to happen before the end of this decade.
The LGA also warned that rising demand for adult social care and children’s services threatened the viability of other services such as street cleaning, libraries and highways maintenance.
LGA senior vice chair Nick Forbes said: “Councils knew they would struggle to cope with the pace of government funding cuts over the next few years. It was hoped that local government as a whole keeping all of its business rates income by 2020 would ease that pressure.
“With those plans now in doubt, councils are faced with the double jeopardy [that] not only the money they have to pay for local services running out fast but also huge uncertainty about future funding after 2020.”
Other LGA demands included publication of the long delayed Fair Funding Review consultation, an end to changes to the New Homes Bonus and abolition of 2% limit for council tax increases above which a local referendum is required.
