Nottinghamshire County Council says it is doing everything possible to keep the number of compulsory redundancies to a minimum.
The local authority, which has to shed 3,000 posts, said 1,700 workers had expressed an interest in redundancy.
The Tory-led council needs to save £150m over the next three years.
But Andy Belfield, Unison spokesman for the East Midlands, said not all of the staff who had expressed an interest in redundancy would want to go.
He said: "It means that they're workers who have expressed an interest in seeing their figures.
"When you think that the average pension in local government is around £4,000 a year, you can pretty much bet your bottom dollar that most people aren't going to bite their hands off and take early retirement...
"They've scared 20,000 people that they might lose their jobs."
But the council's chief executive Mick Burrows stressed that the pressure to make savings was unavoidable.
He said: "We've got to find £39m more for children's and adults' (services) next year, regardless of the government's announcement, and that affects the 500 services we run.
"We're no longer able to run what we have at the moment - 45% of our cost is made up of staffing. If we've got to save that amount of money, we have to take posts out of the organisation."
Mr Burrows added that, where possible, the council was "absolutely avoiding" compulsory redundancies.
The local authority currently employs around 12,000 staff.