A Conservative-run council wants to raise its tax by 15% in the next financial year, blaming government cuts and increased demand for social care.
Surrey County Council leader David Hodge said the government had cut its annual grant by £170m since 2010.
The proposed increase would add nearly £200 to a Band D bill, bringing it to about £1,500.
The government said if the proposed budget is set, taxpayers would have the final say in a referendum.
Any authority wanting to increase council tax by more than 2% must put the plans to a vote.
This would take place on 4 May, alongside local elections, and would include a vote in Chancellor Philip Hammond’s constituency of Runnymede and Weybridge.
Opposition councillors in Surrey said the increase would be unaffordable for many residents and it followed financial failings by the council and the government’s failure to fund services properly.
Council tax analysis – Pete Sherlock, BBC News data journalist
We can’t say what the average rises are set to be this year, as not all local authorities have declared their intentions.
However, last year the average Band D council tax set by local authorities in England for 2016-17 was £1,530.
This was an increase of £46 – or 3.1% on the 2015-16 figure of £1,484 – and 1.6% of that was the adult social care precept.
So Surrey’s rise is five times last year’s average.
This shows how council tax hikes were brought down post 2008, but are now on the rise again.
Mr Hodge said the council had to set a budget for 2017-18 that would protect vital services.
He said: “The government has cut our annual grant by £170m since 2010, leaving a huge gap in our budget.
“Demand for adult social care, learning disabilities and children’s services is increasing every year.
“So I regret, despite us finding £450m worth of savings from our annual budget, we have no choice but to propose this increase in council tax.”
Liberal Democrat leader Hazel Watson said a 15% rise would hit the elderly and those on fixed incomes hardest.
She said: “It is astonishing that the Conservative administration think Surrey residents should carry the can for their own financial failings and the government’s failure to properly fund services.”
The Conservative council had failed in its negotiations with the government, even though three cabinet ministers were Surrey MPs, she added.
Transport Secretary Chris Grayling and Health Secretary Jeremy Hunt are MPs in the county along with Philip Hammond.
A Department for Communities and Local Government spokesman said: “If the council sets this proposed budget, then the taxpayers of Surrey will have the final say in a referendum in May. We should trust the people.
“Our long-term funding settlement means more spending power for Surrey County Council during this parliament, with £3.2 billion to deliver the services that local people want.”
Analysis: Jack Fiehn, BBC Surrey political reporter
For years, senior councillors have spoken out about cuts to the authority’s central grant and the impact on adult social care and children’s services, as well as school places and road maintenance. There has been huge frustration and we seem to have reached a crunch point.
Surrey residents are used to council tax rises. They have gone up every year since 2012 – but never by such a large amount. This will be a test of public support.
The Liberal Democrats, Labour and the Green Party all oppose a referendum, but David Hodge has told me he has the support of his fellow Conservatives.
So unless something significant happens, it is almost certain to go ahead.
He has also denied reports there will be a deal with ministers to abandon the vote, putting the government on course for a row with a council in the Tory heartland.
Former care minister and Liberal Democrat health spokesman Norman Lamb said Surrey’s decision would be a test for local authorities, which were seeing increasing numbers of older people and younger people not getting the care and support they need.
Shadow local government secretary Teresa Pearce said: “Forcing councils to rely on council tax income to fund statutory services, such as social care, is simply unsustainable and unrealistic.”