Government officials estimate 2200 parents will have their benefit cut in the first year of the new regime that will penalise them if they don't send their children to early childhood education centres.
Green Party co-leader Russel Norman tabled a cabinet paper including the estimate in parliament on Wednesday and questioned Acting Prime Minister Bill English about it.
Mr English said ministers didn't agree with the estimate.
"We take a more optimistic view than the officials do in the cabinet paper," he said.
"We think most parents, in fact almost all parents, are likely to comply with those obligations."
The government announced the latest welfare reform on Tuesday, saying beneficiary parents would get three warnings and then their entitlement would be cut by 50 per cent if they didn't send their children to ECE centres when they were three years old.
Opposition parties say it will penalise the most vulnerable families and there will be a severe impact on the children of those families.
"What kind of monstrous government punishes children because it doesn't like the actions of their parents, and is it not a policy of laying the alleged sins of the parents upon their children?" Dr Norman asked.
Mr English replied, "What kind of monstrous government, of which the Greens were part up to 2008, did absolutely nothing for the most vulnerable children and the most impoverished families in this country?"