Ambulance Employees Australia said weary paramedics had fallen asleep at the wheel and administered wrong drugs because they did not have enough time off between shifts.
They have called for a minimum 10-hour break between shifts, compared with eight hours under the current award.
But Ambulance Victoria has said the fatigue issue was one of 175 union claims, which it said sought $800 million from pay talks.
Talks between Ambulance Victoria and the union have broken down.
Mr McGhie said paramedics were angry and felt the government was not listening to them.
"For an entire year we`ve negotiated in good faith for proper rest breaks and fair wages. We have got nowhere," he said.
"All they are seeking is what paramedics in other states already have, longer rest breaks and fair wages."
A union survey of 350 paramedics last year found many only get five hours` sleep between shifts.
Some had fallen asleep at the wheel of their ambulances and admitted to making clinical errors because of the workload.
