It is in Key's - and New Zealand's - interests to show Obama that New Zealand can play a significant and supportive leadership role in overcoming the stumbling blocks to the conclusion of the agreement.
Just why this is important is not widely understood.
New Zealand basically plays a dual role in the TPP negotiations. Not only does the lead negotiator - Ministry of Foreign Affairs deputy secretary David Walker and his team - have to prosecute New Zealand's national interest in the talks, but Walker's team is also integrally involved at the multinational level, fulfilling New Zealand's role as the official "Depository of the TPP".
Trade Minister Tim Groser issued statements on behalf of all TPP parties when he welcomed Mexico and Canada into the talks. Groser's statements were relatively anodyne.
But it is clear that apart from the significant economic gains, New Zealand also has a substantial diplomatic interest in the TPP's conclusion.
One well-placed trade source suggests a positive outcome could be for New Zealand to host the secretariat for the TPP. This would be a substantial international diplomacy gain for New Zealand if it does occur. It would not quite put Auckland - or Wellington, for that matter - on the same level as Brussels, which hosts the EU Trade Commission, or, Geneva, which hosts the World Trade Organisation, but it would be a powerful upside for New Zealand if it can be pulled off.
Other nations - such as Singapore which hosts the Apec Secretariat - will also have an interest. Possibly more so now that former Reserve Bank Governor Alan Bollard is moving to the Apec director's role with a brief to drive the vision of a free trade area of the Asia-Pacific further than just mere rhetoric.
The TPP Secretariat would clearly be an international body and its lead roles would have to be open to competition from around the Asia-Pacific.
But if New Zealand does finally get to host the TPP Secretariat there would be considerable cachet for this nation.
The problem is that while New Zealand is the administrator for the TPP negotiations, the United States is seen as running the overall agenda.
Apart from the US only the leaders from six TPP members were in Phnom Penh: three of the original P4 partners - New Zealand, Brunei and Singapore - plus the leaders of Australia, Malaysia and Vietnam.
On its own this is not sufficient to clear away all the stumbling blocks to the TPP.
These obstacles are the bold proposal to liberalise the agriculture markets of the TPP nations and the push by the United States to make its intellectual property regime the platform for the rest of the Asia Pacific.
The issues are complex and will be on the table when Auckland hosts the next round of TPP talks early next month.
New Zealand's default position has long been to put agriculture gains at the top and centre of trade negotiations.
But there is rising awareness within the business sector that while New Zealand should celebrate further access to major agriculture markets, it must be careful not to concede too much in the critical areas which will underpin the platform for 21st century business.
The upshot of the Obama initiative was not finalised when this column went to press, but the President's desire to get together with the leaders from the six TPP nations present at the East Asia Summit was inspired as much by geopolitical rivalries as America's need to boost access for its exporters to Asia-Pacific markets.
The US is back in Asia with a vengeance.
That much was obvious when Obama and the Asean group (the 10 countries in Southeast Asia) launched a new initiative to expand trade and investment ties.
The US-Asean Expanded Economic Engagement should ultimately assist regional economic integration by providing another pathway for the Asean group as a whole to link up with the Trans-Pacific Partnership.
That's how the White House put it. But the more critical aspect is that it helps Washington solidify its presence in the region.
Basically the US was making it clear it would not be cold-shouldered.
It was still a player in Asia even if it was not part of the Regional Comprehensive Economic Partnership (RCEP) - that was launched yesterday by Asean and six other nations: China, Japan, South Korea, Australia, New Zealand and India.
The big game is important.
If New Zealand does finally get to host the TPP Secretariat it will cement this nation as an important interlocutor in regional trade.
But it is important to note that New Zealand already has trade deals with many of the TPP nations.
The big gains are from cementing ties with the Nafta group - the US, Canada and Mexico and with Japan and South Korea, if they can be persuaded to dock.
Meanwhile, Chinese Premier Wen Jiabao's invitation to New Zealand to sell more goods to China is positive.
Prime Minister John Key gets quite a bit of stick for spending time out of the country promoting New Zealand's access to global markets.
But getting facetime with Wen at the East Asia Summit - even if he will have stepped down by the time Key gets to Beijing next year for the official celebration of 40 years of diplomatic relations - is important.
Key told reporters: "It's not often that you sit down with a leader of a country who has 1.4 billion citizens and he says to you, 'Sell us more goods'."
Key said dairy products, wood products and educating more Chinese students were important points for the Premier.
The big challenge will be elevating meat products and services on to China's priority list.
