Constitutional experts and a ratepayers' group are concerned that councils will be more difficult to control while some could be worse off if local government is formally recognised in the nation's founding document.
Anger is growing over the use of ratepayers' money to help fund the "yes" campaign for the September referendum, with some 50 Victorian councils pledging about $1 million towards a $10 million national fighting fund organised by the municipal lobby.
The Gillard Government has already committed $55.4 million of taxpayers' money for the referendum, including more than $11 million for a civic education campaign to promote the "yes" case.
But Victoria, which along with most states opposes the referendum, says it is a waste of public money and legally dangerous.
"(This is) supported by constitutional law experts Professor Cheryl Saunders and Professor Greg Craven, who state that changes could cause legal uncertainty, blurring the roles and responsibilities between the three tiers of government," she said.
"If this proposal gets up, the State Government's ability to intervene into poorly governed councils like Brimbank could be at risk."
Ms Powell said the Federal Government would spend $55 million on the referendum while cutting budgeted grants to Victorian councils by $13.4 million.
"Ratepayers are now asking why they are paying for the campaign," she said.
Prof Craven, also vice-chancellor of the Australian Catholic University, said that, speaking as a Carlton supporter, "this referendum has more problems than our backline".
"Most local governments are honest and hard-working but every now and then one goes out of control and then the State Government has to step in and re-boot the whole thing by sacking the council and putting in administrators," he said.
"The next time that happens the very first thing that council will say is, 'You can't touch us, we're in the federal Constitution', and the battle will end up in the High Court."
Lord Mayor Robert Doyle accused the states of being churlish and said they had been left flat-footed by the referendum.
"Their complaint was that it was going to create competitive sovereignty and that was the scare campaign they were going to run," he said.
"The Federal Government's wording makes it abundantly clear that local government is still the creature of state governments. They can still be sacked."
Cr Doyle said the constitutional change was a simple mechanism to provide direct funding to councils on projects of national and mutual benefit, such as the planned redevelopment of Queen Victoria Market.
"This might be something where you say to the federal government, this is not just about an open-air fresh food market. This is about a crucial part of Victoria's economy," he said.
Campaigner Tim Wilson, from the Institute of Public Affairs, urged ratepayers to tell their councils not to hand money over to run an irrelevant political campaign while they were struggling to fund services.
He said the constitutional change would make councils more indebted to the federal government, which could then dictate how money was spent.
"Councils will be worse off if this referendum passes because more power will be in the hands of Canberra politicians and bureaucrats, not local communities," he said.
heraldsun.com.au 16 June 2013