Key has ruled out being part of a "military intervention". But he has left open the possibility of New Zealand joining a "training intervention" which the US is expected to table in Washington.
It's been suggested this could be a "work around" - rather like the device that former Prime Minister Helen Clark deployed to send engineers to help in Iraq after the 2003 invasion. The SAS would not be part of the military fighting forces - but a stabilising force nevertheless.
The US economy has been on the turn. But the IMF has slashed its forecast for 2014 economic growth from 2.8 per cent to 2 per cent after a sluggish first quarter.
As Lagarde said yesterday: "What happened is [the first quarter] was dreadful ... our forecast is revised downwards, but our expectations are quite high and positive for the coming months."
On Fox News, Lagarde went on to say that when the IMF looked at big geopolitical risks it also looked at the consequences on the US economy. "We believe the oil shock that could result from the current tension in Iraq in particular might affect the economy." But for that to happen, the shock "would have to be rather deep and rather long-lasting".
The Brent crude oil index climbed 4.2 per cent last week - an indicator of how dependent the world still is on Middle East oil supplies.
It is inevitable that the increasing tensions in Iraq will be centre-stage when Key meets Obama and at his later meeting with US Defence Secretary Chuck Hagel at the Pentagon.
It is important though that this does not overshadow two other major regional and international issues that are important to New Zealand. These are the Trans Pacific Partnership negotiations which have the potential to set the commercial framework for the Asia-Pacific region as well as open more doors for New Zealand exporters to nations which have a protectionist framework.
And climate change where it will be important for Key to stress that New Zealand does not share Australian Prime Minister Tony Abbott's campaign to turn the clock back on measures to constrain carbon-fuelled industries (like coal).
Ahead of Key's visit, Trade Minister Tim Groser would not be drawn on contentious issues such as whether New Zealand would ink a deal that does not lead to zero tariffs on dairy exports.
In Japan recently, Groser indicated that while TPP could stumble if governments finally lacked the courage to confront their highly protected sectors, there was every reason to believe that TPP will be the "decisive influence in creating the entire FTAAP or Free Trade Area in the Asia Pacific".
What Key should remind Obama - who has not been sufficiently focused in winning domestic support for TPP within the US - is Groser's warning that if TPP fails another less developed set of trade talks in which New Zealand is involved, the Regional Comprehensive Economic Partnership, involving China but not the US, would take leadership of the regional integration process, possibly in a two-speed process, implying one would be for ambitious trade liberalisers and another speed for the countries not able to move forward.
Key should remind Obama that this is realpolitik. If the US wants to maintain its regional influence it must focus on economic ties - not be diverted, once again, by the latest security problems in the Middle East.