The opposition has been ratcheting up the pressure, saying Covid-19 is no excuse, as wait times were on the rise well before the pandemic.
Two people have died - one last week in Christchurch and at Middlemore in June - after initially leaving due to long wait times.
Christchurch Hospital's emergency department had double the number of patients it was resourced for on the night a woman died after walking out because of wait times, a leaked email to staff says.
The woman died on Monday last week, after going to ED the previous Sunday evening, triggering a formal review into the hospital's care.
And the parents of a four-year-old who died in Wellington last month are questioning whether he would still be alive if medical staff had acted with more urgency.
National leader Christopher Luxon said those cases were tragic and the result of a "big blow-out" in emergency wait times.
"I think we've gone from something like 9 percent of people waiting more than six hours to see an emergency department to now almost a quarter of New Zealanders having to wait more than six hours."
The government needed to take accountability for the "five years of abject utter failure", Luxon said.
"The outcomes have not been achieved. They've been very, very poor. I can look at emergency wait times, I look at time to get to first specialists, I look at four months or longer to get to first surgeries, every single one of those metrics is going backwards."
National's health spokesperson Shane Reti said he felt for the hospital staff turning up to work each day, knowing they were under-staffed and that they would likely have to do more shifts.
However, he said New Zealanders had to be confident in the system, and the minister.
Reti was asked by reporters if Andrew Little was up to the job of health minister.
"I think a minister who says that the chair of the Australasian College of Emergency Medicine has incorrect data, a minister who challenges an ICU specialist at Capital and Coast on the number of beds that they've got and a minister who says that the nursing organisation speaks with forked tongue is likely to have lost support from the sector.
"I think he is likely to have lost support from the sector, it's gonna be really hard to make progress when you've lost support."
Asked if he would resign in a year's time if ED wait times had not been fixed, Andrew Little said the public would get to have its say at the 2023 election.
He admitted targets to be seen within six hours of arriving at emergency departments were not being met but told the House it had been a particularly tough winter.
"Our EDs are on the receiving end of record presentations this year - over 100,000 in June; over 100,000 again in August - and I stand behind and stand with the amazing health workforce that we have providing care to people, even those who are waiting long periods of time to get that care, and making sure that people get the care that they need."
National is calling for more efficient spending and immigration changes to attract more nurses.
Little said the government had significantly boosted funding for a system left under-funded by National.
