Can we Achieve a Predator Free New Zealand?

If you look at New Zealand's history, it becomes very obvious how good we are at eradicating introduced predators from off-shore islands. Who's to say we can't get rid of predators from Stewart Island by 2020? Or even better - a Predator Free New Zealand by 2040!
SCRIPT:
Maria Island (1 hectare) - cleared of introduced rats by Forest & Bird in 1960 to protect a breeding colony of Storm Petrels. The world's first island rat eradication.
A decade later... the wildlife service gets rid of predators on Titi Island (17 hectares)
By the 1980s, Breaksea Island (170 hectares) becomes the largest Island to be cleared of rats.
In the 1990s, DOC sets a new world record by making Kapiti Island (2000 hectares) predator free.
In the 2000s, DOC breaks its own record on Campbell Island (11,300 hectares).
So... What's next?
Rakiura/Stewart Island (170,000 hectares). We want to see our third largest island predator free by 2020.
Judging by our track record, anything is possible!