The union has warned of deep resistance to cutting local services
Up to 1,000 workers at Sheffield City Council face losing their jobs in the next five years, a BBC investigation has found.
The cuts were forecast as the county's local authorities revealed plans to reduce spending by millions of pounds.
Rotherham Council plans savings of £13m over the next financial year with Barnsley seeking cuts of £5.5m.
Unison said attempts to reduce services in local communities would be met with "deep resistance".
The predictions were made as a result of council responses to the Facing The Cuts survey by BBC News.
The authorities said cuts were planned in anticipation of an expected fall in government funding.
The job losses at Sheffield are expected over the coming three to five years as part of an £18m savings plan.
However, the authority said it hoped to increase council tax by just 1.5% - the lowest ever rise.
Rotherham Council said savings had already been identified in overtime working, procurement and use of agency staff and consultants.
Doncaster mayor Peter Davies's plans for £18m of cuts have been voted down by councillors and the budget for the next financial year has yet to be set.
Chris Jenkisnon, Unison regional representative, said: "The problems of this country are not the fault of the public sector workers, they're the fault of bankers and their greed and it's simply not fair that public sector workers should be expected to pay the price for that.
"They are public services that are lifelines of local communities, which are currently depending on public service workers spending their money and keeping the local economy moving.
"Any attempt to cut those services in local communities will be met with very deep resistance indeed."