Cheshire West and Chester Council and British Waterways say they are seeking urgent talks with the government over funding for repairs to the Sutton Weaver swing bridge on the A56 near Frodsham.
According to British Waterways, which owns the 90-year-old structure, the bridge will soon need major re-strengthening work at a cost of £4m.
The council said it can meet its share of the bill but British Waterways is struggling to find the balance.
Both organisations are seeking a meeting with the Department of the Environment Farming and Rural Affairs, which funds British Waterways.
According to the council the bridge is used by around 20,000 vehicles a day and is on a diversion route when the M56 westbound is blocked.
Cllr Lynn Riley, executive member, community and environment, said: "The bridge plays a vital role in the local transport system – not least as a motorway release valve – and we are deeply concerned about the current situation.
"We are working closely with British Waterways on the issue and hope that a joint approach to Government will provide the help needed to address what could well prove to be a major problem."