The council is consulting on patching up a forecast $295 million budget deficit in this year's budget, with Wayne Brown proposing a mixture of staff and services cuts, including the possible replacement of librarians for volunteers.
Brown said three years ago that 14 million library books were being withdrawn annually but that had now reduced to 4 million books.
He agreed arts and libraries played a role in communities but said everything needed to be trimmed to save ratepayers from filling the hole.
PSA assistant secretary Bronwynn Maxwell said libraries should not be looked at as a leisure service, but an essential source of information and education to communities.
Brown's comment that libraries could be staffed by volunteers demonstrated a woeful lack of understanding about what libraries did, Maxwell said.
"They don't just check out books, libraries are important because they provide everyone access to information and education regardless of socio-economic status or location, using volunteers is simply a recipe for shorter hours and a run-down in services."
Librarians generally have a qualification from the Library and Information Association of New Zealand Aotearoa (LIANZA), while library assistants nearly always had a tertiary qualification, Maxwell said.
Job cuts would impact the functionality of libraries and undervalue the workforce, she said.
Under the Local Government Act councils have a responsibility to promote the social, economic, cultural and environmental wellbeing of the community, she said.
"It's not just libraries under threat, it's a number of other services, those services help us to build communities and the city will only be the poorer if this proposed cost-cutting is carried out."
There were other options for saving money and Brown was "catastrophising" the council budget, Maxwell said.
There could be an increase in borrowing to keep libraries and other services until revenue streams could be brought back online, she said.
"We're really urging Aucklanders to tell the council how much they value their community services 'cause they're under threat."