Jerome York said it was time for GM "to go into crisis mode" and warned that Kerkorian had not ruled out pushing for the carmaker's board to be changed.
Speaking at the Detroit motor show, York added that GM should consider selling its loss-making Saab unit.
GM’s debts have hit $4bn (£2.2bn). The carmaker, which has been knocked by falling sales and high costs, recently announced it was closing 12 US plants and cutting 30,000 jobs.
It has also agreed a deal with unions to reduce its staff healthcare obligations by $1bn (£569 million) a year.
York said Saab was a “pretty consistent money loser” and also questioned the future of the Hummer four-wheel drive vehicles.
"When a company is in deep trouble - and make no mistake, GM is at the present time - there are only so many hours in the day for management to effectively focus on and fix things.
"That focus needs to be on the important levers that can really move the needle," said York.