The survey, conducted after the teacher's 2.7% pay award, shows at least four councils will be making compulsory redundancies. Losses will be heaviest in education and social services.
Targeted at a selection of the worst hit councils, the straw poll revealed that Sheffield is considering shedding 2,000 part and full-time posts to compensate for a £20 million shortfall.
Sheffield lost 1,350 posts last year, 900 through voluntary redundancies, and because it has few older staff, compulsory redundancies are unavoidable this year.
Roger Young, organiser of the county's Unison branch, said: 'We are already down to the bone.'