According to a survey of county councils, the local services most at risk are bus services, home care for older people and climate change projects.
Other services in the firing line include leisure centres and parking.
Rapidly rising inflation and increased demand for services, particularly in social care and housing, have added millions of pounds of extra costs for local authorities this year.
A survey of dozens of mostly rural authorities in England belonging to the County Councils Network found that around a third were "not confident" they would still be solvent in 18 months' time if more money was not provided.
More than half suggested they were likely to look at reducing road maintenance, cuts to home-to-school transport, and changes to either the number or opening hours of libraries or recycling centres.
Many councils are calling on Chancellor Jeremy Hunt to provide more money in his Autumn Statement on Thursday.
The government says it is working with councils to understand how inflation affects their budgets, and funding for next year will be announced shortly.
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