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.