An LGC exclusive by news editor Rebecca Evans and finance reporter Dan Drillsma-Milgrom.
An LGC poll of chief executives, their deputies and finance directors has revealed that more than half of councils - 56% - do not believe the savings target can be met without services being affected.
Only 32% of the 72 councils who responded believe they can make the savings without denting services. A further 12% are not sure.
One council said: 'We have already shaved off any surplus possible. Any further cuts are inevitably going to start affecting services.'
Another said: 'The easy-to-make efficiencies have largely already been exploited and reprioritisation of services is the only way to manage the increased pressures of social services demand, waste and equal pay. Three per cent cashable efficiency targets, low settlement grant floors and capping could prove a lethal combination.'
Gordon Brown set out the 3% target for 2008-2011 in his pre-Budget statement last month. He said the emphasis would be on cashable savings, where money is released by providing services at lower costs.
A total of 62% said they would not be able to increase the proportion of cashable savings they made.
The results showed vast differences in the proportion of cashable savings councils are achieving at present. While 18 said they were delivering cashable savings of 80% or more, the same number said cashable savings amounted to 5% or less of their efficiency gains.
Improving procurement of goods and services and sharing back office departments such as HR are the most popular ways councils expect to make savings. But officers' jobs could also be at risk - 60% of councils said reducing the staff headcount would be among their top three solutions.
David Clarke, director of resources at Warwickshire CC and secretary of the Society of County Treasurers, warned councils against claiming they would not be able to meet the efficiency target.
'I don't think that all the fat has been trimmed. New opportunities are constantly coming up to make savings. I think it is a dangerous tactic for local government to put forward a line saying 'we are as efficient as we could possibly be',' he said.
Chris Leslie, director of the New Local Government Network, said the government must be 'crystal clear' that councils will be allowed to keep their savings. 'We have got to give people an incentive otherwise it is like you are saying: 'Here, run this way down a corridor and then there's a cliff edge at the end'.'
Nearly four-fifths of the councils called for incentives to share services. The most common suggestion was for pump priming to fund set-up costs.
Tony Travers, director of the Greater London Group at the London School of Economics, said the desire for a planning gain levy was 'spot on'. 'It is exactly what Sir Michael Lyons needs to have impressed upon him. He needs to find a way of allowing authorities to capture some of the tax benefits to development so they can hold and reinvest them locally.'