East Sussex CC has warned it may not even be able to provide basic statutory services in less than three years unless the government provides extra help.
It is the second Conservative-controlled council following Northamptonshire CC to announce it may only be able to offer 'core' services next year as a result of government funding cuts and rising demand.
A report to its cabinet says the core offer will provide 'support to those most in need, preserve some level of early help and prevention and assist with the economic development of the county.'
But it says the next three years will see more reductions in Government funding and adds: 'There are many variables, but we may reach this level of service by the end of 2020/21 and there is no guarantee that we will have sufficient resources to deliver even the core offer sustainably beyond that date unless the Government addresses our fundamental funding issues, which we share with much of local government.'
A spokesperson for the Conservative-controlled council told LocalGov: 'We are looking at the possibility of only offering services that we are legally obliged to provide.'
Last week Northamptonshire CC said it would switch to a core offer offering basic statutory services in a bid to plug a £60-70m cash shortfall.
East Sussex CC chief executive Becky Shaw, said: 'Our core offer paints an honest picture of the minimum that we realistically need to provide in the future and we want to use this as the basis for discussion with the government, partner organisations and residents in East Sussex.'
The council said it was looking at a worst-case scenario deficit budget position by 2021/22 of £46.4m.
A spokesperson for the authority said council leader Keith Glazier had written to local government minister James Brokenshire about the 'counterproductive choices' it had been forced to make.
