Cheshire East Council is currently led by a joint Labour and Independent group administration.
Councillor Corcoran said: “The cost-of-living crisis isn’t just affecting individuals, rising costs are also affecting councils.”
He said the council had “specific issues”, including a low level of reserves and the “financial shock” of the cancellation of HS2.
“Labour, and the Independent group too, are absolutely committed to doing everything that we can to keep tight control of the council’s finances, and really difficult decisions will have to be made,” he added.
The consultation will end on 28 January.