The warning came after local politicians delayed making a decision on £73million of cuts until the New Year, with calls for them to hold talks with unions.
Mike Kirkby, the Scottish secretary of the public sector union Unison, is demanding that councillors hold negotiations with workforce representatives before deciding the final programme of cuts.
Services are expected to be hit amid speculation that up to 1,400 council jobs could be axed as politicians consider a range of 280 options which could amass savings of £103.7m.
Councillors are under pressure to agree a controversial budget for the next two years which will result in £73.3m of cuts and, in the run-up to Christmas, delayed making a decision until the turn of the year.
The crucial meeting is expected to be held shortly, although a date is yet to be announced.
John Mooney, secretary of North Lanarkshire Council's Unison branch, said: "Our stewards across the authority have been frustrated by the lack of information and involvement.
"The proposals for cuts to services and jobs need to be looked at. They would destroy the social fabric of North Lanarkshire if accepted."
Union official Mike Kirby warned of a bitter winter of discontent if politicians attempt to sack council workers.
He said: "If North Lanarkshire, or any other council, moves to compulsory redundancies, Unison will consult on industrial action."