Schiller told today's governing body meeting that perhaps the reality of the programme was more to do with saving money than modernising library services.
The ongoing job uncertainty had caused unacceptable levels of stress and loss of moral for library staff, she said.
"This administrative approach cynically disregards the work, the knowledge and the love our librarians provide their branches.
"It is impossible not to reduce service when staff are cut and juggled around," Schiller said.
She quoted a former librarian, who said: "Knowing my position and hours are going to be axed, not knowing what the new positions would look like, where they would be, what hours on what days, the unknown created too much anxiety.
"Also the thought of going up against my colleagues is something that made me feel sick," the former librarian said.
Mayor Phil Goff, who told Newstalk ZB on the campaign trail last year that spending on libraries should not be cut, said there would be no reduction in services or library closures.
Goff said the petition would be forwarded to Council's chief operating officer Dean Kimpton for consideration. The points would be taken seriously and taken into account, he said.
