A message posted by a councillor on Twitter saying his authority was "clearly not cutting enough" has been described as "crass".
Conservative-controlled South Gloucestershire Council agreed £9m of cuts at a meeting on Wednesday.
Councillor Robert Jones, who has apologised for the tweet, posted the message saying: "No sign of protest. Clearly we're not cutting enough."
Liberal Democrat Jon Williams said he was "shocked" by the message.
"This is people's jobs and services - you can't be crass with that," Mr Williams said.
"[Being made redundant] is not a nice thing to go through. I would think that [message] is a bit of a kick in the teeth. It's a rotten thing to do.
"He's probably regretting ever putting that Twitter. It's political suicide."
Union Unison also criticised the message saying it was from "a councillor who takes pride in cuts".
Mr Jones, a Conservative councillor for Bradley Stoke, has since deleted the message from the micro-blogging site.
"I apologise unreservedly for any offence caused by the remarks I made," he said in a statement.
"Prudent planning has meant that South Gloucestershire Council is one of the most well-prepared councils in the country to adapt to its expected fall in central funding hence there being no protesters at the budget meeting."
More than 300 jobs are expected to be lost over the next two years in "back-office posts", according to South Gloucestershire Council.
The council currently employs about 3,000 staff and has a budget of £196m.