I'm listening to the House at the moment, and they seem to be involved in a long debate which turns on the claim by the opposition that the Governor-General might realistically refuse assent to a bill. It's a point which has been quite popular of late in opposition circles (see in particular Matthew Hooten's recent call for a constitutional coup), but it is a monarchical fiction. While s16 of the Constitution Act 1986 requires that bills be signed by the Governor-General before becoming law, the last time the Royal Assent was refused was in 1708 - and then on the advice of Ministers. It has never happened under responsible government, and for a Governor-General to refuse assent to a bill when advised by Ministers to sign it is now simply unthinkable. Even those who do not think it is unthinkable (notably Phillip Joseph) view the power as so tightly circumscribed as to be effectively nonexistent; it is patently not the case (as National is currently asserting) that a Governor-General could wake up one morning and say "I don't feel like signing this". To do so would be to break our most fundamental constitutional convention, that
the Queen reigns, but Cabinet rules, so long as it has the support of Parliament
It is not the role of the Governor-General to be an independent actor or act as any sort of right-wing check on our democratically elected Parliament. Instead, their job is to host garden parties and sign whatever is put in front of them. To see a party openly questioning this in Parliament is stunning, and it shows how radical and desperate and contemptuous of our democratic system the National Party has become.
Update: Lewis has an excellent post on a related point which spells it out:
The Governor-General does not have the ability to refuse Royal Assent to legislation; if not because the power was repealed by the Letters Patent 1917 then by the repeal of the relevant provisions New Zealand Constitution Act 1852; if not by implied repeal then because the Governor-General is bound by the convention of responsible government to act on the advice of the government of the day; if not convention then because the Prime Minister may have the Governor-General recalled by the Queen at any time.
That about sums it up. What we have is the atrophied appendix of a once-absolute monarchy. And for the record, I'm all in favour of chopping it out before it turns septic. If we are to have any form of veto power by the Head of State, then it must be codified and brought into law to act on behalf of the people - rather than left as some vestige of "divine right" to be used against them.