Prime Minister John Key has admitted the National Party faces a "herculean" task to win the Mount Albert by-election.
His party's candidate, Melissa Lee, has attracted criticism for claiming the proposed Waterview motorway in Auckland would divert criminals from South Auckland.
She has since apologised for the remarks.
Mr Key told Morning Report that he will not write Ms Lee off for one mistake.
He says he still has complete confidence in Ms Lee as an MP and by-election candidate.
But Mr Key says he knows it is unlikely she will be able to win the electorate.
The by-election will be held on 13 June. The Mt Albert electorate has been held by Labour since its formation in 1946.