Labour might go up in the polls after Jacinda Ardern's rise to the leadership but in the long run people "won't vote just on a personality", Prime Minister Bill English says.

The morning after having his personality compared to that of a rock by Labour's deputy leader Kelvin Davis, English told Mike Hosking on Newstalk ZB the fallout from Metiria Turei's benefit fraud admission would make a coalition involving the Green Party and New Zealand First "almost impossible".

"What you have seen among Labour, the Greens and New Zealand First is a lot of a shuffling around of the vote, and I think that divisions open up - it is now almost impossible to see Winston Peters and Metiria Turei in some kind of cohesive coalition."

English said National had not got polling back since Ardern took over last Tuesday, but said they were focused on getting their vote above 47 per cent, necessary to "have a good government after this election".

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"In the long run people aren't going to vote just on a personality, they will vote on the issues. And our support has been pretty good but we have to get it higher, that's the poll we are concerned about."

On Davis' quip that English had the personality of a rock, the Prime Minister said it could be taken as a compliment, and might refer to the "rock star economy" under National.

Ardern announced an ambitious plan to build a $3 billion light rail network in Auckland from scratch yesterday, the same day English confirmed a mix of heavy rail and road projects to deal with congestion.

Labour's policy will be partly funded by a regional fuel tax.

In Wellington, Turei launched the Green Party's national Maori campaign, after fallout from her admission she mislead WINZ during her time on a benefit as a solo mother in the 1990s.

Turei on Friday ruled herself out of a Cabinet position. Soon after that announcement Ardern held a press conference and revealed her team had that morning told the Greens that Turei would not be in any future Cabinet.