Had they done so, they might have realised the new (and temporary) law to be pushed through Parliament to block New Zealanders from heading for Syria to sign up with Islamic State (IS) looks like being far less an infringement of personal freedom than its much lengthier and more prescriptive Australian counterpart.
The Greens might have also realised contributing to military training in Iraq was about the minimum John Key could get away with without traditional allies such as Australia looking askance.
Labour Party polling is understood to have shown no appetite among the public for sending combat troops. Even National voters did not like the idea, with less than a third comfortable with that option.
National's private polling would have produced similar results. Mr Key is nothing if not poll-driven. His Government's contribution to the battle against IS is correspondingly very much on the moderate end of things.
However, the Greens would prefer to demonise National as a persecutor of the poor, environmental dinosaur and in this week's case, unfailingly loyal lap-dog itching for an invitation to sign up to Uncle Sam's latest military adventure.
It was hardly a surprise that the Greens rejected every initiative in Mr Key's Wednesday address targeted at IS.
In doing so they have displayed not so much a reluctance to shift on principle as a refusal to entertain even the thought of doing so. That is their right.
But it means two things.
First, there can be no getting the Greens out of the shadow cast by Labour without either compromise or dropping whole swaths of policy as a prerequisite of any move more to the centre of the political spectrum.
It also makes it harder for them to supplant Labour as the dominant party on the centre left.
That is because the politics of Opposition stretch much further than just opposition to policies or ideas.
On occasion - and Wednesday's speech was one - the public expects political parties to show some flexibility so they might reach some consensus in the national interest. This is especially so on foreign policy, defence and intelligence matters.
Labour understands this. The Greens pretend not to understand.
During the debate, Greens co-leader Metiria Turei, who sounded as if she had just jetted in from San Francisco circa 1967, declared her party stood for ''peace and freedom'' (who doesn't?) before adding that peace was the best weapon when it came to achieving personal security.
Just as homeopathy is the best weapon for curing Ebola, presumably.
But never mind.
Ms Turei rejected National's plan to send military personnel to Iraq in a training capacity, arguing that any military engagement, including training was a contribution to the ''war'' effort and would not result in peace.
Neither could the Greens accept the cancellation of passports, the expansion of video surveillance or an extra $7 million for the SIS.
No doubt Ms Turei's rejection of everything in Mr Key's speech made her and her colleagues feel good about themselves.
All they succeeded in doing was to isolate themselves from the mainstream. It was left to Labour to exercise real Opposition.
The party accepted the broad thrust of intended legislation to block those intending to fight for IS through cancelling passports.
But Labour also made it clear it would try to use select committee scrutiny to iron out detail that it is not happy about.
As an example, Labour is worried the new ability of the SIS to conduct surveillance in an emergency without a warrant for up to 48 hours will become the norm, rather than the exceptionl.
Like the Greens, Labour is questioning the wisdom of New Zealand training Iraqi soldiers.
But that is because Labour believes the poor state of the Iraqi armed forces is the outcome of too much meddling in the past both from the local elite and the period of the American occupation.
Labour can thank three senior MPs for the party's assured and no-fuss handling of the kind of issue where sticking to long-established principles, as the Greens have done, can be of no practical use to anyone.
Those three MPS are Annette King, Phil Goff and David Shearer.
The former is revelling in her role as ''deputy acting leader'', which she will relinquish when the result of the party-wide leadership ballot is made public in 10 days' time.
In the meantime, Mrs King's vast experience and innate political savviness - attributes she shares with Mr Goff, Labour's defence spokesman - have seen the pair ensure Labour is seen as acting responsibly and not bagging the Government just for the sake of it, but without attracting scorn on their side of the fence.
They have been greatly assisted by Mr Shearer, who worked for the United Nations in Baghdad before returning home and entering Parliament.
His knowledge of Middle East politics in general and Iraqi politics in particular gives him real authority as Labour's foreign affairs spokesman, a role which has seen him grow in stature, in contrast to his difficult days as party leader.
The irony is, not a few within the party believe Mrs King and Mr Goff are well past their use-by date - and they would not be shedding any tears if Mr Shearer exited with them.
It is the Greens who are the losers, however. Mr Key's speech offered them a heaven-sent opportunity to get closer to National.
But they have wasted.it.
They have instead reinforced the perception that they are too soft when it comes to how best to respond to the Prime Minister's response to the threat to life and limb posed by the jihadists of IS.
And they have been taught a lesson that being in Opposition is not solely a matter of opposition for opposition's sake.
• John Armstrong is The New Zealand Herald political correspondent.
