Hikes in council tax are testing the patience of homeowners, local government minister Nick Raynsford has conceded.
Pensioners are already taking to the streets over the tax
Mr Raynsford told the Sunday Telegraph bills were reaching the "limit of acceptability" for many families.
"The increases in the last two or three years have really taxed the patience of a lot of people.
"They have been very substantial increases and we have to look at options for change," he said.
He spoke as two other Sunday newspapers warned of unrest and even "riots" over the issue.
Council tax bills rose sharply this year, with increases averaging nearly 13% among English councils, and there have been growing signs of public discontent.
Some pensioners - including a group of about 300 in Devon and Cornwall - have begun refusing to pay, saying they are prepared to go to jail instead.
Mr Raynsford said earlier this week that the government would not cap council spending this year, but may do next year, if councils keep trying to raise the tax.
However, on Sunday he said the government was preparing to allow councils to raise money in other ways.
In particular, he said the government was considering allowing councils to keep £1bn over three years from business rates, which currently go direct to the Treasury.
Council tax has nearly doubled in 10 years, while pensions are up by just a quarter
A Band D house - reckoned to be an average home - now has a typical annual council tax bill of over £1,000.
Last week the Devon
and Cornwall Police Authority warned of possible civil unrest over the high bills.
The Sunday Express says the Association of Police Authorities is so concerned such unrest could spread nationally, its chair Ruth Henig has written to the government to urge more funds for policing.
The letter, to Home Secretary David Blunkett, reportedly said: "There comes a point when council tax payers will no longer support such increases, and their member authorities are increasingly telling me we are reaching this point."
The Mail on Sunday quotes Jim Wilson, chair of the Norfolk Police Authority, warning deputy prime minister John Prescott of "resentment and potential civil unrest".
This weekend, two charities representing older people called for council tax reforms, saying they were effectively discriminatory against pensioners.
Council tax had nearly doubled in the last 10 years, whereas most pensions had only risen by a quarter, they said.
The average household spends 3% of its income on council tax, while for pensioners the figure is 6%, they said.
One protesting pensioner, 68-year-old John Peerless, recently staged a 48-hour vigil outside Plymouth Magistrates' Court to point out that while his pension had gone up 1.7% in 12 months, his council tax had risen 13.4%.
The Local Government Association, which represents local authorities, says councils have had to spend more to make up shortfalls from holes in government funding.