Hamilton City councillors were accused of looking after a "sacred cow" after refusing to look at ways of slashing $500,000 from the Waikato Museum's budget.
Councillors voted 6-5 against plans to trim public and education programmes run by the museum.
Proposals to extend the length of semi-permanent exhibitions from three to nine years were rejected as "boring".
It was the first major hurdle in the city's plans to cut costs by $14.5 million over the next three years.
Councillor Gordon Chesterman said he did not think he would be alive to see the next exhibition at the museum if the term was extended to nine years, and Daphne Bell said it would be like showing only Terminator 3 at the movies for a year.
Mrs Bell also said plans to cut up to 33 jobs would remove "skilled and able" staff from the city.
But Ewan Wilson told fellow councillors that not making hard decisions could lead to the "horrible predicament" of having to sell art collections.
"There should be no sacred cows. Every one of these issues we have to grapple with."
Margaret Forsyth said councillors had cut 23 per cent from community development but were dithering over cutting 10 per cent off a $5 million arts budget.
The council approved other tough calls, including a 20 per cent fee rise for building consents.
Planning fees and charges will rise 25 per cent.
A $40,000 reduction in noise control services was reluctantly approved, as councillors acknowledged its contribution to making city living enjoyable.
An increase in dog registration fees from $74 to $89 over three years was approved.
Discussions on service cuts and fee increases for Hamilton Zoo and the city's swimming facilities were deferred to the next Long Term Plan meeting on Tuesday.
The 2012-22 long term plan will be put out for public consultation in March.
Fee rises
* Food outlet registration and inspections up 5 per cent
* LIM reports up between 64 and 100 per cent
* Planning fees and charges up 25 per cent
* New fee for re-inspections of non-complying food premises
* New consultancy fee for resource consent
* Building consent fees up 20 per cent
* Dog registration fees up 6.5 per cent or 20 per cent over three years.