A cross-party campaign has been launched by Scotland's councils to fight for a better deal on finance from the Scottish government.
They have also called for the reform or replacement of the council tax, to give them a secure level of funding in future.
Local authority representatives have said they are struggling to maintain core services.
But the Scottish government said it had treated local government "very fairly".
Finance Secretary Derek Mackay will set out his budget on 12 December.
Alison Evison, the president of the local authority body Cosla, said: "Looking across Scotland, it's services that local government deliver that will end up having to suffer.
"We're talking about libraries and support services, we're talking about mending roads and cutting verges, play parks and leisure centres, about all the things people need in their lives.
"When we're talking about extra pressures on vulnerable people, with universal credit coming in, we're seeing increasing social isolation. We deliver so much to individual people as well as communities."
The councils have said higher council tax can meet some of the budget shortfall, but Cosla is inviting all Scotland's political parties to join it in talks early next year on how to reform or replace that tax.
The issue is likely to be part of negotiations on the draft budget which get under way at Holyrood next month.
Cosla vice-president Graham Houston added: "Are we at the cliff edge? I would say yes, and it's not that we're advancing, it's advancing towards us through erosion.
"There are some smaller councils that are at that cliff edge, will find difficulty setting a legal budget, with no reserves.
"They're very restricted in what they can do about it."
A Scottish government spokesperson said: "Councils provide a range of essential local services. Despite continued UK government real terms cuts to Scotland's resource budget, we have treated local government very fairly - and in the current financial year they received a real terms boost in both revenue and capital funding.
"We have made clear that we are open to further dialogue on options for local tax reform.
"The finance secretary will present the Scottish Government's tax plans in the Scottish Budget later this year."