''It keeps on coming back," he said.
The trust said in a statement that consultation undertaken by the council over the last two years had been exhaustive and included workshops, interactive sessions, presentations and surveys.
There had been consistent and strong community support for a museum and the community was getting tired of being asked the same question over and over again, it said.
Barclay said the decision to go to a non-binding referendum was, on one level, unfortunate because it pointed to a lack of resolve and leadership.
But now the decision had been made to run a referendum, it was a chance for people to deliver an emphatic message they expected the council to deliver a modern city for present and future generations, he said.
''This included a high-tech museum that celebrated our past, our future, and told the world the story of who we are. We need this focus as a city - to move beyond being a port town that is some sort of satellite of Auckland.''
Barclay said the trust had supported the study that resulted in the council naming Cliff Rd as the preferred option.
The promoter of the referendum, Tauranga's deputy mayor Kelvin Clout, agreed it was a turning point.
Clout said he favoured a museum because of the massive social and cultural benefits and economic flow-on from tourism. People coming to live in Tauranga also expected a city this size to have a museum.
He expected these feelings would be reflected in the referendum, together with resistance from people who did not see value in a museum and were focused on the level of their rates.
''It gives people a real opportunity to make a stand on this issue and to make an effort to open their envelope.''
Clout was referring to the council's decision to piggy-back the referendum on the council by-election to find a replacement for Gail McIntosh who died recently.
''I am confident this will increase the turnout - it will add a lot of interest to the voting process.''
He disagreed the referendum displayed a lack of resolve and leadership by the council. ''It's an opportunity for democracy in action.''
Clout said the referendum would not slow the Long Term Plan (LTP) decision-making process. ''We are going through the LTP consultation process anyway and this is another input into the process.''
Responding to social media critics, he said the council was not legally allowed to make it a binding referendum because it was going through an LTP process and the referendum could not cut across that process.
A museum on Cliff Rd
- Estimated cost $55.65 million.
- Council contribution capped at $20.65 million.
- Projected visitor numbers per year 240,000 in 2023.
- Peak traffic of 45 buses and 540 cars per day.
Source: Tauranga City Council