Councillor Don Thwaites was the sole councillor who voted against the extra funding.
"I'm dead against this as the extra funding source would come largely from debt, and as far as I am concerned the whole process is rotten to the core," he said.
Councillor Margaret Murray-Benge said it would be "absolute nonsense" to suggest that council should not approve the extra funding for such a vital "precious" asset.
"We fund so many other community projects when there are cost overruns and we have got to do so here as concept two clearly meets the needs of the Katikati Community.
Councillor Karyl Gunn-Thomas said she would reluctantly support the extra funding request but only if she could be assured the project would be achieved in budget.
Councillor John Scrimgeour said he also supported the concept two option reluctantly.
"That's because I have always believed in the concept of doing something once and doing it right," he said.
Katikati Library Community Reference Group spokeswoman Jenny Hobbs questioned how the budget could blow out so badly, and told councillors she wanted some accountability.
"At our first meeting, we asked for and received assurances that the concept would be possible within the budget," she said.
After the meeting Mrs Hobbs told the Bay of Plenty Times the revelation the build was unaffordable came as a huge shock.
"I'm so thrilled that council has supported the extra funding amount and shares our vision of creating an iconic building which will serve the community for the next 50 years.
"However we really want council to closely scrutinise the costings of this project and the architect's build, given there has already been a $1m cost overrun."
How the project would be funded:
Loan $2,294,510
Finance contributions $765,000
Asset replacement reserve $540,000
Special Reserve $200,000
Subsidies and grants $350,000
Community roadings $150,000
Community reserve $200,000
