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In his State of the Nation address on Monday, Mr Cunliffe set out a policy to give most parents of newborn babies a payment of $60 a week until that baby turns 1, while those on middle and lower incomes would continue to receive the payment until the child turns 3.
He said the first year payments would apply for those with household incomes of less than $150,000 a year, which Labour estimated will be about 59,000 households or 95 per cent of children aged under one.
Labour also plans to extend Paid Parental Leave from 14 to 26 weeks.
What Mr Cunliffe failed to clarify in the speech was that parents won't be eligible for the $60 dollar a week baby bonus while they're on paid parental leave.
He told TV3's Firstline this morning that he denied misleading the public.
"Our materials which we published at the time of the speech made clear right from the get-go that people have a choice; they can either take the baby bonus ... for the whole year, which they're entitled to do ... that's what the speech said, or - if they are also eligible - they can choose to be on Paid Parental Leave, which is a greater amount. So they're never going to be worse-off than the $60 dollars a week.
"One word in the speech could have been different - 'will' or 'can' - not a big drama.
"We've been absolutely frank and absolutely clear in all the materials for this speech that people have the choice between going on the $60 a week for the whole first year or taking Paid Parental Leave if they qualify. They can't do both. At no point have we said that they could do both."
Speaking on Firstline yesterday, Prime Minister John Key attacked Mr Cunliffe's credibility.
He accused the Labour leader of "misleading New Zealanders" over the proposed child payment scheme.
"David Cunliffe's developing a reputation around Parliament for being very tricky," Mr Key said.
"He [Cunliffe] just needs to learn to be up front with the public so they can actually trust his word.
Mr Cunliffe said today the Government is losing the argument in substance, "so they're indulging in disappointing, personal attack."
- Additional reporting by Claire Trevett