Uncertainty was also making it difficult for them to prepare accurate 10-year plans, five chief executives said in a joint statement.
They called for better funding tools and for the new government to quickly understand the challenges faced by the sector.
"The key issue is a fundamental disconnect between what councils are being asked to deliver, and the funding tools they have available to pay for that delivery."
The statement was signed by Dunedin City Council chief executive Sandy Graham and district council chief executives Mike Theelen (Queenstown Lakes), Peter Kelly (Central Otago), Steve Hill (Clutha) and Alex Parmley (Waitaki).
Not on that list was Gore District Council interim chief executive Stephen Parry, but he had already made his thoughts plain.
The planning environment was so uncertain — in large part because of upheaval connected to Three Waters reform and an expected reversal in government policy over it — it might be best to cancel development of next year’s long-term plan, he suggested.
Mr Parry described a "sea of uncertainty" about Three Waters, coupled with stress and fatigue on local councils, given funding pressures and the reform agenda advanced by the last government, and he said confidence levels were low.
Councils are mostly funded through rates on property, fees, charges and government subsidies.
The system has long been criticised as inadequate, as councils are required to provide infrastructure, facilities and services amid cost pressures and constrained funding.
The five chief executives who signed the joint statement picked up on similar themes to Mr Parry.
Councils faced the uncertainty of being asked to deliver a 10-year plan — the most significant document councils prepared, involving thousands of hours of staff time — without knowing what the future held for key reforms facing the sector, including Three Waters, they said.
It was a task also made more difficult by the cost of living crisis and inflationary pressure.
"These challenges are not going away, and all councils are grappling with the need to manage short-term cost pressures while continuing to invest in core infrastructure maintenance and development, to avoid longer-term service failures and funding crises," the chief executives said.
"We need a better mechanism for local government funding, not just a delay to the next 10-year plan, and we’re hoping to engage with the incoming government quickly to discuss these issues."