The Otago Daily Times conducted an informal poll from Friday, August 13 to Sunday, August 15 asking readers if it was time for the mayor to resign.
The poll drew 157 responses and 129 people, or 82%, believed he should resign.
Approached yesterday to comment on the result, Sir Tim replied by text message.
He said given the "avalanche of criticism" directed at him over the past week, he was not surprised by the results.
"It is hard to represent my side of the story without running down other people, something I am trying to avoid.
"Hearteningly, I am overcome with the number of people telling me to hang in there and not to let the bureaucrats wear me down."
The mayor has shown no intention of resigning.
In the 2019 election, Sir Tim beat runner-up Darren Ludlow by more than 3000 votes, receiving a total of 9672 votes.
Last week, tensions boiled over when he labelled the organisation a "regime" and claimed he had been left humiliated by staff going through personal documents.
The comments followed the revelation that Sir Tim, who has been Invercargill’s mayor for nine terms — 22 consecutive years — was storing personal items in council-owned buildings across the city, and that boxes of old papers had been thrown out.
Deputy mayor Nobby Clark suggested the situation had reached a tipping point and indicated a vote of no confidence could happen soon.
Meanwhile, a six-month review of the council’s progress addressing the issues highlighted in the Thomson Report was due to be released later this week.
The report, by former Dunedin city councillor Richard Thomson, highlighted issues including Sir Tim’s struggle to fulfil significant aspects of his job, the relationship between the mayor and the council chief executive, and the appointment of Cr Clark as deputy mayor.
Poll result