If Raymond and Emily Hoche-Mong had delayed their Edinburgh holiday until next month, they might have been greeted as the millionth visitors to the Scottish Parliament since it opened nearly 30 months ago.

Instead, the retired San Francisco couple were visiting yesterday, learning for the first time of the cost controversy, as attempts were made to put it to rest. "They all do it," said Mr Hoche-Mong, a former construction manager. "They all go over budget. But it's an extraordinary statement that Scotland is making with this building. It won't get lost in anything else."

American tourists don't have to pick up the £414m bill, but the impact of critical acclaim from ordinary visitors and from architectural experts has changed perceptions of the parliament since it was opened. Those who work with public visitors say feedback is around nine parts positive to one negative, particularly after people see inside the building.

The internationally prestigious Stirling Prize in October 2005 capped a run of eight major awards, and the critics enthused. Deyan Sudjic in Prospect magazine, wrote the parliament emerged from its scaffolding "as one of the finest pieces of new architecture in Britain for 50 yearsa lyrical and complex composition of oak, granite and steel". Icon magazine stated: "It is one of the most extraordinary buildings built on these islands in recent years, both in richness of detail and the breathtaking quality of the workmanship."

Meanwhile, to Emily Hoche-Mong: "It's an amazing, wonderful building. I'm so glad it's new. It's not trying to look old, like everything else around it."