Council chief operating officer Dave Foster told councillors a contract would soon be signed with Fletcher Construction after six companies expressed an interest in the project.
He said the council could not afford any delays and as long as the final quote came in on or under budget staff needed council sign off to approve the quote and begin work.
"The absolute details of the contract have not been determined because we are still at the stage of detailed design, however if we don't go for pre-approval it's going to significantly stall the timelines for the completion of the project given how much construction time is required."
Mr Foster said if there were any issues with costs staff would come back to the council for further discussions.
But, Mr Kent said the whole project should be stopped and the incoming council should have the final say after October's election.
"I consider spending $8.8 million worth of ratepayer money when we can achieve a health hub and reconditioned library for about $4.5 million is totally irresponsible.
"I also object most strongly to what I see here is very plainly an attempt to ensure this process cannot be stopped by an incoming council."
Mr McVicker also questioned the original funding figures and if the health board could actually afford construction costs.
Councillor Janet Wepa, who is on the project's working party, said some comments against the project were misleading, especially regarding costs, and it had come back to the council at least twice since it was tabled under the long-term plan.
"It went through as a majority decision ... the vote didn't go the way of some councillors and they don't like that."
Councillor Karen Hunt said it had been a rigorous process and to suggest otherwise was "simply mischief making".
"It is within the funding envelope ... and has been analysed to the Nth degree.
"It's also a bit of mischief to say we could do it for around $4 million, this was before we understood the magnitude of the problems in the building.
"It is going to go forward and this is just business as usual for our council."