"If we don't fix these things and look to the long term, we'll be putting a cap on our own growth," said Quinton Hall, chief executive officer of Ngai Tahu Tourism, one of the country's biggest adventure tourism operators. "We've got a natural cap on our peak period right now because we just don't have the accommodation in New Zealand. Even if they wanted to come, they couldn't find anywhere to sleep."
Tourist numbers jumped 12 percent in 2016 and are forecast to reach 4.5 million by 2022 -- almost matching the country's current population of 4.7 million. Government research last year identified a likely shortage of more than 4,500 hotel rooms by 2025, after taking into account existing construction plans for about 5,200 new rooms.
Hotel occupancy in Auckland averages 94 percent in February and about 86 percent over the year, with the nation's largest city frequently full.
"If immediate solutions aren't found, it is unlikely we will continue to grow at current levels," said Dean Humphries, national director of hotels at Colliers International. "If we are going to continue to see more tourists come into the country, where do they go?"
In the regions, the influx is causing different problems, with infrastructure like car parks and toilets straining under the load.
At the 12-mile (19.4-kilometer) Tongariro Alpine Crossing, a trek through a World Heritage Area on the central North Island volcanic plateau, thousands of tourists are overwhelming facilities designed to be used by a few hundred people a day.
In Glenorchy, near Queenstown, where Ngai Tahu offers jet-boating, canoeing and horseback trail rides, the company is forced to bring in chemical toilets during peak season because the small town's waste-water facilities are insufficient.
There's a similar issue at Franz Josef, the South Island township near the spectacular glacier of the same name, where untreated sewerage was pumped into a nearby river after a surge in tourist numbers.
The overloading is fueling concern that a bad tourist experience will harm New Zealand's clean-green image and dent an industry that earned $10 billion (NZ$14.5 billion) from foreign visitors last year -- a fifth of all export receipts.
Funding the infrastructure that's required is now sparking debate.
Many of New Zealand's natural attractions are remote, and the nearest towns don't generate enough local taxes to pay for the car parks and rest stops visitors need.
Regional councils this week estimated NZ$1.4 billion needs to be spent on tourism infrastructure to keep pace with demand. The government, which disputed that figure, has allocated NZ$17.5 million. The association representing tourism operators wants more, noting that foreign tourists contribute NZ$1.15 billion annually to the government's coffers in sales taxes alone.
Christopher Luxon, Air New Zealand's chief executive officer, said last year he supported a national bed tax and a border levy on visitors to help fund tourism investment.
There are also growing calls for visitors to pay to enter national parks, as they do most days at the Yellowstone and Grand Canyon national parks in the U.S.
"We provide all sorts of things free of entry, but not free of costs," said David Simmons, professor of tourism at Lincoln University in Christchurch. "We need an informed discussion about user pays."
Solving the accommodation shortage will be in the hands of private investors such as Auckland International Airport Ltd. and Tainui Group Holdings. They are building a 250-room five-star hotel near the international terminal under Accor SA's Pullman brand, due to open in late 2019.
Until then, Jenny Nuku can expect more calls for emergency lodgings at Te Puea Marae, whose entire hall can be rented for NZ$500 a day. That's less than NZ$10 per person for the 53 American tourists who bedded down there last month and got the added bonus of an authentic encounter with Maori culture.
"They said they'd traveled around New Zealand, and this was the first real cultural experience they'd had," Nuku said with a chuckle. "They had their phones and iPads out, taking selfies. We were just happy to be of assistance."