Both Canada and the US impose high tariffs - as high as 300 percent in some cases in Canada - along with small quotas for total imports, and American dairy farmers have lobbied vigorously against opening their market up to competition from Fonterra, which they paint as monopolistic and anti-competitive.
"For New Zealand to do a deal, it has to be a deal on our terms," said Key, who met with TPP countries' leaders, including re-elected US President Barack Obama, on the fringes of last week's East Asian economic summit, where a new commitment was made to conclude TPP negotiations in 2013.
New Zealand was a prime mover in establishing the TPP initiative in 2007, which the US later joined, and which has become a priority for the Obama administration as it seeks to engage more deeply with the Asian region and to stimulate its own economy.
"President Obama is deadly serious about wanting to do a deal," said Key. "He believes he can get a deal done."
But New Zealand could not sign up to a deal that excluded dairy exports, the country's largest industry.
Following the US elections earlier this month, Obama's Democratic Party controls the US federal Senate, where much opposition to TPP has come from in the past, although the Republican Party controls the federal Congress, the US Lower House of Representatives.
Other TPP negotiating nations are Singapore, Australia, Mexico, Brunei, Chile, Peru, Vietnam, and Malaysia, with Thailand signalling at least week's summit in Cambodia that it also wished to join. Japan is also continuing to show interest.
At the same meeting, New Zealand signed up to negotiation of a separate trade pact, the Regional Economic Cooperation Partnership, which includes the countries of the Association of South-East Asian Nations and China, but not the US.
However, RCEP is seen as likely to take longer than TPP to conclude and is less committed to what trade negotiators call a "high quality" agreement which seeks to limit the extent of special exclusions to meet member countries' trade sensitivities.
Opponents of the TPP are conducting briefings in Wellington and Auckland this week, in concert with the Green Party.