Senior MPs are angry at Mr Cunliffe's apparent lack of repentance for Labour's dismal result in his concession speech when he appeared to avoid taking blame, and instead used it to launch his own re-election bid.
Yesterday he conceded it may have been a mistake not to take the Green Party up on the offer to campaign as a joint force in the election.
"In hindsight, the progressive forces of politics probably would have got a better outcome if they had been better co-ordinated."
In an apparent attempt to get a headstart on any likely rival, Mr Cunliffe effectively started his re-election campaign on election night by sending out an email to the party members and unionists who vote on the leadership.
In that email, obtained by the Herald, he said the party needed to refresh and modernise. "That's why I will be seeking a new mandate from the party, the affiliates and the caucus by the end of the year."
He said he would be in touch with further information, and signed off using a union term "in solidarity, David Cunliffe".
Labour's rules require Mr Cunliffe to get 60 per cent support from his caucus in a confidence vote, which is unlikely.
There is little doubt he will be contested - Grant Robertson, David Shearer and David Parker have all refused to publicly state their intentions so far. Another possible contender Andrew Little said his defeat in New Plymouth meant he did not feel he had the mandate to run for the leadership this time, even if he had been considering it.
Former Labour Party president Mike Williams said Labour's dismal result at the election could prove fatal for Mr Cunliffe.
"I've always thought that there were three elements to a campaign - there's organisation, there's policy and there's leadership," Mr Williams said on Radio New Zealand this morning.
"I think the organisation was certainly better than last time - I saw a lot more activity on the ground.
"I think that the policy was relatively bulletproof and I don't think the National party scored any particular points off that. That really only leaves leadership."
Mr Williams said he gave Mr Cunliffe his vote at Labour's last leadership challenge and didn't know if he would do so again.
"Personally at the moment I don't think I'd go with David Cunliffe again - this is a historic defeat, it's the worst Labour vote since 1922 - I think there are people in the wings who could potentially do a better job.
"I'm talking about Grant Robertson, I'm talking about David Parker."The party also needed to review the way it selected its leader, Mr Williams said.
Watch: Cunliffe: 'Not a good result'
Last year the leadership process cost the Labour Party about $80,000 - something it could struggle with so soon after an expensive campaign. One MP said the issue should be the interests of the party, "not saving David Cunliffe's arse".
Despite requests from Mr Cunliffe's office to stay quiet, several of Labour's more centrist and right wing MPs were yesterday criticising the direction the party had taken. Those MPs included Clayton Cosgrove, David Shearer and newly elected Stuart Nash, who said Mr Cunliffe should call the confidence vote straight away.
Mr Nash said he believed Mr Cunliffe should test his mandate, and quickly. He also took a veiled swipe at Mr Cunliffe for making excuses for the loss, saying there were no excuses for hitting 25 per cent.
Another MP questioned what "change" Mr Cunliffe intended given he had promised change last year. "The only change was from 34 per cent to 24 per cent."
Mr Shearer would not rule out a challenge for the top job again himself. "What we don't want to do is jump into some form of leadership contest before we've had a chance to sit down and work things out." He said the result showed the party was not talking about issues that affected middle New Zealand and issues such as the man ban had damaged it.
What Labour needs to do
Former Labour President Mike Williams:
* review party organisation, including fundraising methods.
* stop navel-gazing.
* stick to organisation, policy and leadership. Williams gave them two out of three this campaign. "Leadership is going to be the most difficult of all."
Former candidate Josie Pagani :
* replace officials such as President Moira Coatsworth and General Secretary Tim Barnett after two failed campaigns.
* head back to the centre, abandon the failed strategy of focusing on the left to try to capture the 'missing million' voters.
* talk to a wider audience, don't get bogged in identity politics/ factions.
