Government support partner Peter Dunne faces a battle to keep his seat in the Wellington electorate of Ohariu.
A One News-Colmar Brunton poll released on Sunday shows the UnitedFuture leader a long way behind Labour's Greg O'Connor - the former Police Association president running in his first election.
Mr Dunne has held Ohariu since 1984 but scraped in by just 710 votes in 2014.
The poll indicated 63 per cent who voted for him last time were voting for him again, but 27 per cent were switching to Mr O'Connor and 10 per cent were picking another candidate.
Mr Dunne is aware his support may have been eroded but isn't voicing any concerns yet.
"I am not going to get too carried away or excited at this stage because I think there is a lot more water to flow under a rather big bridge," he told the Herald on Sunday before Sunday's poll.
National Party campaign manager Steven Joyce believes many Green supporters will have switched their support to Mr O'Connor.
"We've got a job to do to encourage people to support Peter, primarily because he helps bring strong stability to the government," he told TVNZ's Q+A programme on Sunday.
Mr Joyce wasn't yet reaching for the "cup of tea" publicity stunt, which has been used in the Epsom electorate to urge National supporters to vote for government allies.
"The moves tend to happen quite late," Mr Joyce said.
ONE NEWS-COLMAR BRUNTON OHARIU POLL:
* Labour's Greg O'Connor - 48 per cent
* UnitedFuture's Peter Dunne - 34 per cent
* National's Brett Hudson - 14 per cent
* TOP's Jessica Hammond Doube - 2 per cent
* National - 46 per cent
* Labour - 35 per cent
* Greens - 12 per cent
* NZ First - 4 per cent
* 501 eligible voters polled. Margin of error of plus or minus 4.4 per cent.