CUPE Local 79 is voting on what the city is calling a take-it-or-leave-it offer and union officials say the results should be tallied by late tonight or early Thursday morning.
Local president Tim Maguire says the city has threatened to unilaterally impose terms that would erode workers' basic rights if the offer is refused.
But he says it's unlikely any job action would take place before Friday at the earliest and stresses the union would rather head back to the bargaining table.
Members last week gave the union a strike mandate but said they had no immediate plans to walk off the job.
Deputy mayor Doug Holyday says the city's offer is "fair, reasonable and affordable," and close to the deal that was accepted by the city's outside workers.
Maguire was not ruling anything out this afternoon.
"It's now a very real possibility that the city would impose terms of employment, so we have a very real possibility of a strike here," he said.
The inside workers include child-care workers, ambulance dispatchers, nurses, janitors and parks and recreation staff.
The two sides are in a legal strike-lockout position.
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