Unison branch secretary Jon Rogers said the service was 'very dramatically understaffed'. More than 80 library staff had taken redundancy over the past year, largely due to problems with the management direction, he said.
The service needed more workers, and unless an agreement could be reached with the council in the next fortnight there would be a strike ballot, he said.
Library staff went on strike for five days earlier this year. Planning staff are due to vote on strike action over proposals to dismantle the environmental services directorate.
Staff left for a variety of reasons and it did not indicate there was a problem with the management, she said.