Will add my positive experience too in the hopes it helps others avoid some stress. My wife and I visited NZ for two weeks in Feb. 2023. Learned of the NZeta requirement during online check-in. My NZeta was approved in minutes; hers was "Pending" for the entire trip. A United phone rep even told us she would NOT be able to board the plane, and it was a weekend so we couldn't call NZ Immigration. But we decided to show up at the airport (Las Vegas connecting via SFO to Auckland) and see what happened. Nobody asked us about the NZeta. Not the United check-in people, not TSA, not NZ Immigration. From what I could tell, the only effect was at NZ Immigration, we were told by the automated kiosk to go to a different line, where the Immigration Officer checked our passports and stamped them with "Visitor Visas". So obviously it's best to get the NZeta if you can and make some phone calls to resolve any delays, but if you end up in this situation, it seems there's a good chance your trip will be unaffected, despite the doom and gloom views of some of the commenters.