Councillor John Edwards issued the warning as he was re-elected as chairman for a fifth successive year yesterday.
Councillor Mohammed Idrees, a Labour member of Birmingham City Council, was re-elected as vice-chairman of the authority.
Mr Edwards said the authority was facing increasingly difficult times. The authority faces cuts of at least £14m over the next three years.
He added: "We are at tipping point. I am calling on the Government to listen to our very real concerns that fire stations and fire engines might have to go, and that firefighters will lose their jobs.
"It calls into question our continuing ability to provide the effective and efficient fire service, and five-minute response time, that people in the West Midlands expect and deserve.
"In July, we might get an indication of our likely grant settlement in the Chancellor's budget, but are unlikely to get the details until December. We obviously can't sit back and wait, and are already planning."