Residents in Flintshire are facing a potential 15% rise in council tax or the loss of frontline services.
The warning comes as Flintshire council tackles a £15m hole in next year's finances.
Cuts to a number of services have been earmarked by the council, but it still anticipates a deficit of £6.7m.
The authority is launching a social media campaign next week, #BackTheAsk, to lobby the Welsh Government for an extra £5.6m.
The Welsh Government announces the final settlement for local authorities next month.
'No other options'
Council chief executive Colin Everett warned that even with additional money council tax was likely to increase by about 7%, according to the Local Democracy Reporting Service.
"All committees have agreed there is no room for further reductions in their portfolios next year," he told a corporate resources scrutiny committee meeting.
"It shifts the options over to Welsh Government funding and council tax. There are no other options on the table.
"The local government settlement is grossly inadequate, full stop."
Flintshire council is among the authorities hardest hit by Welsh Government real-terms funding cuts next year.
Council leader Aaron Shotton said: "It's fair to say Welsh Government is awash with capital and there is the potential for a discussion of how that capital alleviates our budget pressures."