It could happen.
Between now and the finale she will conduct the campaign of her life.
From the outset, New Zealand will promote Clark as the best person for the job, not the best person if the Eastern Europe bloc fails to coalesce around a single candidate, but the best candidate, full stop.
That failure of consensus is already evident from the fact that no fewer than six candidates from Eastern Europe have been nominated.
New Zealand will argue that time is up on the regional rotation system. With the complexity of problems confronting the word, it cannot afford to appoint anyone other than the strongest candidate for the job, of either gender, and that Clark is the best.
Key is banking that other leaders see the need for the UN to have someone with a deep grounding in foreign affairs, a focus on results, and a strong leader who can exercise power astutely.
Key's promotion of Clark is heroic. Just when you think he has exhausted his repertoire of superlatives, he finds another reason to say why she is best for the job.
Key met ambassadors from EU countries for breakfast on Wednesday. He will be pressing Clark's case in a private dinner with Chinese president Xi Jinping. (Hu Jintao was president when Clark's Government negotiated the free trade agreement with China).
New Zealand won't be promoting Clark as a woman candidate.
With several highly rated women in the field, and no male who is clearly better than the rest, there will be no excuse to appoint yet another man.
New Zealand will promote Clark as the best person for the job, not the best person if the Eastern Europe bloc fails to coalesce around a single candidate, but the best candidate.
Antonio Guterres, a former Portuguese Prime Minister and former UN High Commissioner for Refugees, is well regarded, but no more so than Clark or Susana Malcorra, Argentina's new foreign minister and a top aide to Ban Ki-moon, who is evidently planning to enter the contest, or Irina Bokova, the Bulgarian who heads the UN's cultural agency, Unesco, and is said to be favoured by Vladimir Putin.
Danilo Turk, a former president of Slovenia, is the second-best fancied candidate from Eastern Europe, but being a man is a distinct disadvantage in this contest.
That may not be enough to deter former Australian Prime Minister Kevin Rudd, nor the fact he could not hold a Government together for a term.
He had been privately campaigning for the UN job while denying he was doing so - until Foreign Minister Julie Bishop confirmed it a couple of weeks ago.
She has effectively given him a deadline of the end of next week - when candidates will each meet the UN General Assembly - to declare before the Cabinet decides who to support, if anyone.
It would be highly controversial for the Australian Government not to nominate Rudd if he asked but the prospect of it backing him is already dividing Australian opinion - which says it all.
His record in the contest so far epitomises his record in politics - brilliant at self-promotion but a disaster as a unifying force.
The contest is wide open because the process is wide open.
In the old days, you just needed to impress the Security Council, which recommended the candidate.
The insistence of the General Assembly of all 193 members to be involved in the selection means Clark will mount a campaign on several fronts:
First, she will run a popular campaign for public support using social media and civil society for the influence it may have on the General Assembly itself. Then she will try to win the support of the General Assembly for the influence it may have on the Security Council. Then she must win over the influential players who are not members of the Security Council, such as India, Indonesia and Germany.
Special attention will be paid to the two classes of Security Council members: the elected members - Angola, Malaysia, Spain, Venezuela, Egypt, Senegal, Ukraine and Uruguay - and the five permanent members especially China, Russia and the United States who wield their veto powers more often than France or Britain.
McCully's personal contacts built up over seven years as foreign minister will be an asset in the Clark campaign. He is travelling to France, Germany and London in the coming weeks.
He is trying to set up a meeting with Russian Foreign Minister Sergei Lavrov, possibly in Moscow. If it comes off it will be the first visit by a New Zealand minister since the annexation of Crimea from Ukraine in March 2014. Clark herself will be meeting key leaders and foreign ministers.
Assisting her campaign will be a dedicated team of officials in Wellington and New York, the Wellington unit headed by senior diplomat Bernadette Kavanagh (the daughter of former Prime Minister Jim Bolger), and in New York by former Foreign Affairs and Trade deputy secretary Craig Hawke, who has taken leave of absence from UNDP to assist.
Whether or not she gets to toast success later in the year, it won't be for lack of effort.
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