As things stand, the council’s projected budget shortfall for 2025/26 is £29m but the figure could hit £77m in three years unless savings targets are met.
Councillors want to save £41.5m by boosting income and making the authority more efficient, and about £2.3m in direct cuts.
Proposals to raise income include generated £1.5m by increasing public parking charges to “align with those in privately-owned car parks”.
Fines for littering could also go up from £150 to £180, while re-tendering the contract for council-owned digital advertising screens could raise £1.35m.
But most significantly the council was looking into changing social care charges “so that those with the most assets pay the full cost of their council care”, a council spokesman said.
The move would not apply to those in temporary or permanent care home places, but those who are cared for at home, and could raise £7.5m over the next three years.
The savings plan also suggested £2m could be saved on staffing with the removal of posts which have been vacant for a year.
Ms Johnson said: “Labour must keep its promise to deliver multi-year funding settlements which would help councils like ours across the country.”
A public consultation on the savings options is open until 12 January, with the final budget to be set by the council on 28 February 2025.
