Calderdale Council has reduced the amount of money it spends each year by £40m since 2010.
But the authority estimates it still needs to find another £40m in additional savings over the next few years.
In five years the council expects the savings it needs to make will rise to £84m, almost one-third of its 2010 budget.
Cuts have already started to effect services, including museums, libraries and car parks, but the council leader is warning of more to come.
Labour leader Coun Tim Swift said: “Anyone who thinks that we can deliver these levels of savings without a severe impact on services to local people is fooling themselves.
“While the council has been doing all it can to try to preserve frontline services, we are facing an extremely difficult situation, with drastically reduced budgets.
“Clearly, this is bound to have an impact on services right across the council and this is at a time when our communities face a whole range of issues, from tackling youth unemployment and keeping our children and young people safe, to making sure that our older and more vulnerable residents receive the care they need and deserve.”
Deputy leader Coun Janet Battye said: “I’ve no doubt that there are even harder times ahead and this underlines the value of making certain that we make the best of the resources that are available to us.”
The council has prepared a financial strategy report for 2013-14 to 2015-16 which warns that it will need to take some tough decisions on spending.
A council spokesman said the authority faced “more uncertaintly than ever” because of the lack of a three-year financial settlement from the government.
The council will present its draft budget proposals for consultation in January, with the final budget presented a month later.
Members of the council’s cabinet will meet next Monday to discuss the finances.