Prime Minister John Key is tipping David Cunliffe to win the Labour leadership.
Mr Key has timed his departure to Europe next week to ensure he will get to face the new leader's first question time.
The results will be announced on Sunday a few hours after voting closes.
The House is in recess this week and resumes on September 17, the day Mr Key leaves.
He said at his post-Cabinet press conference yesterday he made sure he wouldn't be leaving until after the new leader's first day in the House and, asked who he believed would win, he said Mr Cunliffe.
Tonight's candidates meeting in Christchurch is the last for the three MPs contesting the vacancy, Mr Cunliffe, Grant Robertson and Shane Jones.
Last night's meeting was held in Blackball on the West Coast, the spiritual home of the union movement and Labour Party in New Zealand.
A 3 News poll last night suggested that the fact Mr Robertson is gay affects people's perceptions of his chances of winning an election.
When asked whether public opinion about his homosexuality affect his chances of becoming Prime Minister, 58.5 per cent said yes and 41.5 per cent said no.
Among Labour supporters in the poll, 48.3 per cent thought it would affect his chances.
Mr Robertson said the poll asked voters to read the minds of other New Zealanders and say what they think other people think.
"What I experience from people themselves is that they don't view this as an issue." When people were making their minds up, they believed the strongest leader would be the person who could show the best political judgment and lead Labour to victory.
"Yes there will be some people in our community for whom this is an issue and I say to them 'judge me on the policies I am putting forward and on the values of the Labour Party which I believe are the right ones for New Zealand'."
Mr Cunliffe has been ahead on all of the public opinion polls with Mr Jones second and Mr Robertson, the present deputy leader, third.
Four of the six smaller affiliated unions have recommended Mr Cunliffe, but none is insisting its delegates vote for him.
The two biggest unions, the Engineering Printing and Manufacturing Union and the Service and Food Workers Union, whose combined votes will make up just over 11 per cent of the total votes, are leaving it up to members and delegates to vote.
Mr Robertson said more service workers turned up at the Wellington meeting than any other. He was confident of their support and of good support from the EPMU as well.
Former Labour leader David Shearer resigned on August 22 after his core caucus supporters withdrew their confidence in him.
*Voting closes for the new Labour leader midday Sunday.
*The results will be announced a few hours afterwards.
*Prime Minister John Key has delayed his departure to Europe to face the new leader's first question time.