Talks began in 2010 but strong public opposition to the deal here centre on concerns about its impact, such as making pharmaceuticals more expensive. Thousands of people demonstrated in August, many angry that detail of the deal has been kept secret.
The last round of talks in Hawaii in July ended with three issues outstanding: vehicles, dairy and patents on pharmaceuticals.
Key acknowledged this week the deal fell short on dairy but said yesterday it was still likely to be "bigger" than the China Free Trade Agreement, worth $20 billion a year.
It is understood that Key's team are ready to launch a charm offensive on the agreement, in response to outspoken TPP critics such as University of Auckland's Professor Jane Kelsey.
Kelsey and seven other applicants, are seeking a declaration that Groser acted unlawfully when he issued a blanket refusal of an Official Information Act request for information relating to TPP negotiations. The hearing is taking place in the High Court in Wellington.
Kelsey is wary of skyrocketing health costs should the TPP go ahead.
"The stark reality is that any such deal would cost New Zealanders' lives," Kelsey said yesterday.
Media reports in the US yesterday said the deal was close and US President Barack Obama had called Australia's Prime Minister Malcolm Turnbull to discuss it.
Once signed, the leaders of the countries involved will have to turn their attentions to selling the deal domestically after the controversy over the secrecy of the talks. It will also have to be ratified by each country's Parliament.
The Labour Party has said it will not support the TPP unless it meets key considerations, including allowing future governments to restrict land sales to foreigners and a meaningful deal for farmers.
If the deal is not done today, there will be one last chance, at Apec in the Philippines next month.