National is maintaining its grip on rural New Zealand, the latest Fairfax Media-Ipsos political poll suggests.

It out-polls Labour in most rural areas except the upper-South Island, which includes Marlborough, Nelson, Tasman and the West Coast, although Labour's healthy lead in that area may be due partly to a smaller sample size.

The poll shows National remains ahead in the electorally crucial Auckland region, and is also strong in both urban and rural parts of the Bay of Plenty.

But the race is tighter in urban areas in the middle of the North Island, which includes Manawatu, Taranaki and Waikato - though rural voters in those areas remain firmly in National's camp.

The poll shows Labour leader David Shearer shaking off a torrid first year in the leadership, and inching into contention to lead the next government, despite continuing doubts about his performance.

But National's support is still holding up, and it is only a lack of obvious allies that puts its prospects of a third term on a knife edge.

The poll puts National on 44.9 per cent - 1.3 percentage points down on our last poll in December, and back to where it was last August.

But the big story is Labour's slow rise under Shearer.

The party is up 1.9 percentage points to 36.3 per cent, 3.7 per cent higher than in August.

The rise comes despite dissent within the ranks, heavy criticism of Shearer's leadership style, and a leadership challenge, all within his first year on the job.

Labour has now closed the gap with National to just 8.6 percentage points, compared with 20 points on election night 2011.

With Labour allies the Greens making up the shortfall on 10.7 per cent, the poll points to a much tighter race in 2014.

On today's numbers, it would be a dead heat between a National-led bloc and a Labour-led bloc in a 122 seat Parliament.

That's a big concern for Prime Minister John Key, whose present allies the Maori Party, ACT and United Future are unlikely to return in numbers, if at all.

NZ First is below the 5 per cent threshold - though no one is writing it off yet - while the Conservative Party is next on 1. 6 per cent, ahead of Mana, the Maori Party, ACT and UnitedFuture.

Key came out of the blocks aggressively this year with a sweeping ministerial reshuffle and an announcement on apprenticeships designed to appeal to middle-New Zealand.

But he may have misstepped by not demoting his Education Minister Hekia Parata, who has joined a long line of former education ministers in becoming the MP most voters love to hate.

The Fairfax Media-Ipsos poll asked 1000 voters if Key should have moved Parata aside from the education portfolio and 60 per cent agreed.

That rose to 70 per cent among voters from Canterbury, where on Monday she announced a proposal to close or merge 19 schools.

Yesterday more than 1500 school supporters delivered a motion of no confidence in Parata's record to date to the Education Ministry's offices in Christchurch. It followed an NZEI rally in the city.

The dismal public rating comes after a series of political calamities. A plan to increase class sizes was met with derision last year, and resulted in a backdown. A failure to deal with the ongoing problems with the Novopay payroll system saw criticism heaped on her - and Education Secretary Lesley Longstone quit.

Parata was further humiliated when Key gave responsibility for the debacle to senior minister Steven Joyce.

- © Fairfax NZ News