The US sphere of influence is very well maintained and the US Government will not tolerate deviation, it would be surprising to not see diplomatic pressure applied onto New Zealand. The US may not invade NZ in the sense you're thinking but NZ going to get the US Government's attention (which is rarely a good thing).
Given that New Zealand scoffed at allowing US nuclear powered vessels to harbor at their ports, it is unlikely that anything short of direct military intervention will sway the New Zealand attitude. Any politician who is seen appeasing the US would likely answer to the electorate in the next cycle.
Sort of. Please excuse the excess of history if you are familiar with it. Prior to changing their leader, the National party (who now govern NZ) leader said to an American senator that our nuclear policy would be 'gone by lunchtime' if the National party got into power.
www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=10008905 It did and Brash was elected, but Brash has somewhat cooked his goose since then.
The pressure from the US remains however, and the law remains unchanged.
www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=10836045
