Translated to seats in Parliament, National (58 seats), the Maori Party (1 seat), Act (1 seat) and United Future (1 seat) would just reach the 61 seats needed to form a Government.
Labour (33 seats) and the Greens (15 seats) would come up short, even with the support of New Zealand First (12 seats).
That calculation is on the assumption the minor parties win an electorate.
On the preferred Prime Minister question, Bill English rose by 1.2 per cent to 26.2 per cent.
Winston Peters was next most favoured at 9.7 per cent (up 0.8 per cent).
Labour's deputy leader Jacinda Ardern fell 3.9 per cent to 6.6 per cent, putting her behind leader Andrew Little on 7 per cent (down 1.3 per cent).
On May 25 the Government delivered its election year Budget which included $2 billion worth of tax cuts and boosts to Working for Families, which would benefit about 1.3 million families by an average of $26 a week.
Asked if they supported National's family incomes package, 67 per cent of respondents said they did, with 26 per cent saying no.
The poll was conducted before this week, when Labour leader Andrew Little released new immigration policy designed to slash net migration by 20,000 to 30,000 a year.
The Newshub Reid-Research poll has a margin of error of 3.1 per cent.
