Up to a fifth of local councils may put up council tax next year despite David Cameron warning it would be a "huge mistake" to opt out of a Government offer to freeze it.
A survey of town hall finance chiefs by the Local Government Chronicle (LGC) found a fifth were undecided whether to adopt the scheme - while 4% had already decided not to.
Among those expressing doubts, two-thirds were at Tory-controlled councils.
It was confirmed last week that the Government would again offer one-off grants equivalent to a 2.5% hike in the levy to councils which did not raise bills.
Last year, the scheme was adopted across the board meaning average Band D bills remained at £1,439 following significant rises in previous years.
Changes to the terms of the offer have left local politicians nervous about the longer-term implications of repeating the exercise however.
Unlike the previous tranche, there will be no funds provided to protect councils against knock-on effects of the freeze in future years, local government bosses have warned.
One finance director of a Tory-controlled district told the magazine that the deal "financially makes no sense" and would result in a bigger-than-planned hike the following year.
"But politically members feel they've no choice," he added.
Others said deeper service cuts would result.
Based on responses from 146 finance directors, 116 said their councils would implement the freeze, six councils said they would refuse and 24 remained undecided.
Of those who expressed an opinion on the knock-on effects of accepting the cash, 29% predicted a bigger rise in subsequent years, 18% additional savings or cuts and 18% no effect.
Councils in London and the south east were most likely to implement the freeze with the north east showing most doubt, the survey suggested.
Among those committed to decline the cash - and instead impose a 3.5% rise - is Green Party-run Brighton and Hove.
Asked about the decision at Prime Minister's questions yesterday, Mr Cameron said: "It is a decision for individual councils.
"If they want the money to go ahead with the council tax freeze, the money is there, but if they reject it, as they plan to in Brighton, that is a huge mistake, because the council will be asking families in Brighton to pay more at a time when it should be on their side."
Local Government Minister Bob Neill said: "Under Labour, council tax more than doubled, pushing typical bills to £120 a month.
"This Government is helping freeze council tax for two years, as well as abolishing Labour's plans for an expensive council tax revaluation which would force up bills.
"Town hall bureaucrats who want to hike the cost of living and shun the freeze are showing contempt for hard-working families and pensioners."