More than 30,000 people across the Wakefield district are caring for loved ones without pay, according to figures put forward by the council's ruling Labour group.
Councillors from the party are set to call on the government to "get on" and publish much delayed plans for the future of social care funding.
Local authorities are creaking under the weight of the rising cost of looking after an increasingly elderly population. But Theresa May's administration repeatedly postponed the unveiling of new proposals on the issue.
And Councillor Faith Heptinstall, Labour's Cabinet member for health, has highlighted the unpaid carers stat - which equates to nearly one in 10 of the district's population - as elected members prepare to discuss the matter at a meeting next Wednesday.
A motion put forward by Coun Heptinstall says: "Our adult social care system is under unsustainable pressure.
"Major reform of the care system is needed if we are to meet the needs of every adult who requires support appropriately and effectively and end the growing social care crisis."
A senior council officer recently said that delays to the bill were causing nervousness among healthcare companies in the private sector, and stifling investment.
Andrew Balchin, Wakefield's corporate director for adults and health, also said the authority "had given up" on trying to get an answer about when the government's plans might be unveiled.
Coun Heptinstall's motion adds: "Investment in our health services is always welcome.
"However, the government’s current sticking plaster approach to funding social care through short-term handouts makes it difficult to plan for the medium to long-term.
"Unless social care is properly funded, thousands of older people will continue to fall through the net, adding to the pressures that we have seen rising every year on our local hospitals."
Local Democracy Reporting Service