But what are they supposed to do when costs become incompressible and yet for demographic or other reasons existing revenue sources cannot cover them? Parliament cannot amend the laws of arithmetic.
One of the problems with the reliance on a property tax for half of local government's revenue (on average nationwide) is that the twin trends of an ageing population and declining home ownership mean a growing proportion of ratepayers will be elderly, with limited income growth from which to pay ever-rising rates bills.
The Prime Minister's response was that councils allow cash-strapped elderly ratepayers to capitalise their rates bills so they get paid, eventually, out of their estates.
The spectacle of council staff scanning death notices for fiscal reasons is not an edifying one.
And what about the problem, about which the Auditor General has raised a red flag, of a widening and potentially multibillion-dollar gap between the depreciation of existing infrastructure and the expenditure on renewing it factored into councils' long-term budgets? Infrastructure deficits are easy to run up but a costly nightmare to address when you can't do that any longer.
The Prime Minister is relaxed, however. Councils had been funding infrastructure for a long time, he said. They didn't seem to be carrying excessive debt and in any case owned assets - the implication being that they could sell them.
The Local Government NZ discussion paper released on Monday tells us that the biggest-ticket item of councils' operational spending is roading (17 per cent). Another 14 per cent goes on water supply and waste water and 12 per cent on public transport. These are averages, however, and mask wide variation among local bodies.
The challenges Auckland faces in providing for a rapidly growing population are entirely different from those of the 32 local authorities whose populations are expected to decline over the next 15 years. These are often areas with ageing populations and lower average incomes.
A persistent sore point is the propensity for central government to impose responsibilities on local government without any contribution to the increased costs they thereby incur, or any evident consideration of how those costs might be met.
For example new environmental standards for freshwater management will require councils to upgrade their infrastructure, especially storm water and sewerage networks.
Local Government NZ acknowledges that local communities will benefit from cleaner water.
But it argues that some of the benefit accrues at a national level because clean water, like decent roads, supports industries of national importance like agriculture, horticulture and tourism.
Co-funding of the required infrastructure by the taxpayer would recognise that, and the co-funding of local roading, which includes mechanisms for recognising differences in regions' capacity to pay, provides a model for that, it suggests.
If the Government sets its face against new taxes, local government will have little option but to work its existing funding options harder.
Expect to see more pressure on differentials, the system where businesses pay higher rates and rural residents lower rates than suburban residential ratepayers.
The LGNZ discussion paper also questions some of the exemptions from rates that current law requires, particularly on land owned by airports, ports and the railways which are, after all, commercial ventures.
The paper suggests greater scope for user pays. Prices empower consumers and can lead to efficiency gains in a way that funding through taxes or rates does not.
It cites Tauranga's experience with water metering, introduced in 1999. Average water use per household has fallen by a quarter, conserving the resource for other uses and ensuring that the existing system will meet the city's needs for longer than it otherwise would have.
Auckland collects $6 in user charges for every $10 of rates, compared with $9 in Hurunui and just $2 in the Far North.
On development contributions, levied on developers to recoup some of the capital costs of providing the infrastructure their developments require, the LGNZ report quotes the Auditor General's forecast that over the 10 years to 2022 the $3.4 billion collected will cover half the spending incurred.
The paper acknowledges practical difficulties in having new standalone local taxes. But that leaves the option of allocating a portion of the national income tax or GST take to local government "to recognise the role of local government in supporting regional economic activity". Germany and Australia have figured out how to do this.
Similarly, a share of the royalties central government receives from extractive industries would recognise the local costs incurred supporting those industries.
Resistance to all this in the Beehive seems to reflect nothing more than the fact that it seems to be an essential political skill to impose costs, but get someone else to present the bill.
• Local govt cash revenue (2013): $9.49b
• Share from rates: 49%