He would set out clearly what his plans for the party were at those meetings, saying the party's parliamentary arm would be a "significantly different operation to the one we've had".
"We are just going to have to be so switched on and so clear about what our mission is. We will need much, much better organisational systems and to empower every MP to give their best in a co-ordinated way."
Mr Cunliffe would not confirm reports he had offered Shane Jones the finance portfolio as part of the lobbying for support, but said he was not averse to the idea. "I don't think Shane has yet made up his mind what he's doing. I think he's thinking through a number of options. Shane is a very credible potential leader in the economic area. "He is extremely credible in the boardrooms of the country and very well regarded by the business community."
Mr Jones was considering running as a deputy leader but has not yet announced whether he would do so or stated who he was supporting.
Mr Shearer said he was also still talking to MPs to win them over, but would not say how many he had committed.
He would not comment on speculation his deputy would be Grant Robertson, saying he had not yet made a decision. "I'm still really contemplating that at the moment."
Mr Shearer said Mr Parker's withdrawal increased his chances, especially because Mr Parker had openly thrown his support behind him.
Mr Parker withdrew from the race on Friday, understood to be because his preferred deputy Grant Robertson changed his support to Shearer, with others who had supported the Parker/ Robertson ticket.
Mr Shearer said he would set out some more detail about his plans for the party at the meetings with members, but intended to listen to feedback. "I do actually think the right process now is being on receive rather than transmit."
There has been a concerted online growing noise of support for David Shearer since he put his name in the hat on Monday, especially on social media, including comments on Labour MPs' blog Red Alert and by right-wing bloggers.