The total cost is expected to be $147 million in 2015/16 and over half a billion by 2018/19, according to Labour.
Mr McAnulty said it is a solution to the problems facing the people of the Wairarapa.
"Unemployment remains stubbornly high. Wages are not keeping up with costs," said Mr McAnulty. "These are tough times for working families in Wairarapa."
He said nearly all Wairarapa families earn below the threshold, meaning almost every family with a newborn will receive the benefits.
Wairarapa Advocacy Service Advisor, Trevor Mackiewicz, thinks the policy is "a positive thing", and could "make a big difference".
"It's better than nothing," he said. "Young mothers need help to buy nappies and whatnot. People are struggling, they need the money now."
He thinks this proposal might not be enough. "They'll definitely need it beyond three years," he said.
Mr Mackiewicz said his clients range from single parents, to couples with two incomes, to young families beginning their family.
"We've got families budgeting with us because they just can't cope," he said. "We even have people with two incomes coming to us for assistance and advice because they need the help."
United Future leader Peter Dunne supports the extension of paid parental leave and the plan to provide free antenatal services, but described the $60 a week benefit as "a crass bribe".
Following the release of the policy, Steven Joyce, Minister for Economic Development, said Labour "want to start bribing people with massive extra spending. Mr Cunliffe needs to be straight-up about spending taxpayers' money." Additional reporting, NZ Herald.
