Hammersmith and Fulham Council is being asked to pay at least £64m towards repairing Hammersmith Bridge.
The Department for Transport (DfT) has asked the council to meet 50% of the estimated £128m to £163m needed to reopen the bridge.
The 133-year-old bridge was closed entirely in August after cracks in the structure worsened during a heatwave.
The DfT said the council was "responsible for the maintenance and repair" of the bridge.
A DfT spokesman said: "A lack of proper maintenance throughout the years has led to this situation."
The council, which is expecting a £13.7m shortfall this year, warned residents may see council tax double to cover costs.
Meeting the cost could mean an £800 increase in council tax for each local resident.
This "Bridge Tax" would see the Band D council tax rate rise by 71% and an annual Band A council tax charge more than double, the council said.
The authority said the demand was harsher than costs imposed on other councils for large bridge repairs elsewhere in the country.
The council pointed out that the government has funded between 77% and 94% of bridge upgrades in Northumberland, Cleveland, Warwickshire, Staffordshire and Dudley this year.
Motorists have not been able to use 133-year-old Hammersmith Bridge since April 2019 after inspectors found "critical faults" in the cast iron casing.
Pedestrians, cyclists and river traffic were banned from using the bridge more than a year later as its condition had worsened.
The DfT said repairs cannot begin until the council submits a "funding proposal on how a local contribution might be raised".
Stephen Cowan, the council leader, called the demand a "cruel, unusual and unprecedented punishment".
Mr Cowan said: "We are as desperate as everyone else to get the bridge open again.
"But £64m is a level of funding that neither the people of Hammersmith and Fulham nor any other borough can afford even in the best of times.
"We couldn't afford it before the pandemic and we certainly can't afford it now."