Council tax bills in Cornwall may have to rise by 11% next year, because of a funding shortfall of £2bn, according to Cornwall County Council.
The council is due to set its budget in February
It said that unless it receives substantial additional funding next year, bills will have to rise or services will be cut.
Wages in the county are £100 a week less than the English average.
The Local Government Association (LGA) has said it is unlikely the government will be able to help.
Spokesman Sir Sandy Bruce-Lockhart said: "The £1bn extra the government put in last year was a one-off injection of money. It's not recurring, so this year we start with that £1bn problem which brought council tax down before the general election."
Last year several authorities faced being capped by the government which said an "unreasonable burden" was being placed on council tax payers.
But Cornwall County Council said it is facing one of the worst funding crises in its history, with a £13m gap between its current spending plans and an affordable increase in council tax.
David Walley, the council leader said: "Cornwall has always suffered from being a low wage economy, which has a major impact on the amount people can pay for the services they receive."
He said because of this the council had consistently set low levels of council tax for the past five years.
"Every year this has left us with the almost impossible task of balancing the level of services we provide against the community's ability to pay and we cannot carry on like this", he added.
Mr Whalley said the council is having to deal with huge pressures in many of its services, crumbling library buildings, and the major challenge of dealing with the county's waste.
The council is not due to set its budget until February, but Mr Whalley said it will face two stark choices of either raising the council tax to plug the deficit, or making deep cuts in its services.
Devon County Council said it was too early for it to give any indication of the level of next year's increase.
The Office of the Deputy Prime Minister told BBC News the settlement for local authorities had not yet been announced.
A spokesman said: "It will be in due course, but until then it is pure speculation."