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This is not a non-issue. Every time you need to apply for a visa to New Zealand or any other country you will have to explain that you have been refused a visa, and give details of the circumstances. Don't be tempted to omit the details. If the country to which you are applying already knows you have been refused and you omit the information, you'll be considered to be attempting to deceive the immigration authorities and it's likely to land you with a long ban and even more trouble with visa applications. This is particularly true of the Five Eyes countries: New Zealand, Australia, the US, Canada and the UK.
It will have a negative impact forever, if only because it's something else the ECOs have to consider. How much of an impact depends on the exact circumstances of the refusal, and what visa you're applying for. If your circumstances have changed so much that the reasons for refusal have no relevance any more then another application could well succeed.
That impact can be mitigated by building up a travel history. I'm guessing you're a US citizen, so many places are accessible to you for short visits without a visa. Showing that you have a history of visiting countries and complying with the rules will raise your credibility, although even for visa-free entry you should be prepared to answer questions about your refusal.
On a personal note: getting residency in New Zealand is not easy - I know, I did it. Applying for a lesser visa, like a two-year work permit, is easier and could provide a basis for residency later. Some people I know here have been here for ten years or more, renewing their work permit every two years.