The former PM is in the country promoting a new film on her own run for the UN.
In the latest 1 NEWS Colmar Brunton poll, National slipped back three points to 44 per cent.
The 1 NEWS Colmar Brunton poll puts the Greens below the 5 per cent threshold and political editor Corin Dann says the implications could be huge.
Result leaves Greens below five per cent threshold needed to return to Parliament. National are also down.
The Greens leader took to Facebook saying the 1 NEWS Colmar Brunton poll result "is clearly not great news" for the party.