The medical director of Labtests, Gary McAuliffe, said it was processing 10 times more tests than normal.
It had been planning for a possible surge since the last outbreak.
It was moving admin staff, would temporarily recruit university scientists, had repurposed lab equipment from other areas and was getting help from labs in other parts of the country, he said.
Apex Union laboratories organiser David Munro said long hours were standard all over the city at the moment, with social distancing difficult in the packed labs.
"Some of the processes requires people to be in full PPE and they're sweating like a pig, as one delegate said to me," Munro said.
McAuliffe said it would be hard for people to continue at the current pace beyond this week.
If demand stayed high, the Ministry of Health should consider reducing routine testing for other conditions around the rest of the country so labs had more capacity to help with the Auckland Covid response, he said.
Munro warned occupational overuse conditions could set in because of the high rate of repetitive work - like placing samples in machines, or taking caps off them over and over again.
Testers had been asked to screw caps tightly onto samples after one came loose and spilt in a lab - but now some were screwed on so tightly, technicians sometimes had to use pliers to get them off, he said
The aging IT systems and machines were vulnerable to breaking, causing big delays if the testing number stayed high, he said.
The College of Pathologists president Michael Dray said it has been impressive to see labs - and the people that staff them - step up
It was hard to know how long the current surge would last and whether similar situations would become the "new normal", he said.
Lab scientist and union rep Bryan Raills said his colleagues at Counties Manukau DHB were among those working huge days.
People were happy to go the extra mile for now, but they could not sustain that forever, he said.
The Ministry of Health said it was not considering reducing routine tests in other parts of the country, but it was looking at increasing testing capacity and was encouraging doctors not to order non-urgent testing at the moment.