Dudley Council has said it may hold a referendum to ask residents if they are prepared to pay higher council tax.
Council leaders, who say they are facing £29m of cuts over the next three years, say they need to increase rates to keep running all the key services.
Ministers have said that any councils that want to increase council tax by more than 2% must ask their electorates if they are willing to pay it.
The council is surveying residents to get an idea of how they would vote.
The Labour group, which took over the running of the council in May, said that when the 2013-14 budget was drawn up by the previous council administration it assumed that council tax could be put up by 3.5% to help meet the shortfall.
The council is now sending out questionnaires to residents and holding an online poll to get a steer of how people would vote in a referendum, which would cost more than £100,000 to hold.
Council leader David Sparks said he wanted to ask people if they would be prepared to pay a rate rise of 2%, 3.5% or 4.6%.
He said: "We know people don't want to pay the money but we also know they don't want us to close libraries, leisure centres and those sorts of things.
"We're asking, 'how much do you want to us to put council tax up by and what do you want to protect?'"
Local government minister Brandon Lewis said the council had not yet received its grant for next year from the government.
He said: "They should be waiting for that and then looking at what their costs are."
He said the council was "wasting" taxpayers' money by effectively holding a mini-referendum over whether to hold a referendum.