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.
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