"That means he doesn't have financial obligations to the state to actually be paying child support, so it's actually quite a big thing to be dropping that."
National Party leader Bill English said absent fathers could take advantage of the change.
"Clearly there's an opportunity for a father of the child to put pressure on the woman to not name him, so he doesn't have to contribute."
The Government would need to explain the purpose of dropping the sanction, he said.
"It fits in with the notion around child support that the absent parent, generally a father, has responsibilities. The system can't enforce those responsibilities if they don't know where they are.
"Lots of Kiwis go to work every day, work hard, pay their tax. They're willing and able to support those who need it, but want a sense of reciprocal obligation."
He said National would oppose law changes that upset that mutual obligation.
Bennett added that there were already safeguards in the system to protect solo mothers.
"If you can't name the father, then they weren't expected to. They do not get penalised, and there are exceptions around domestic violence and rape and things, where there are valid reasons for a women not the name the father."
The Government has not set a time-frame around welfare changes, but Bennett cautioned about moving too quickly.
"I would hope that they slow down a little bit. I notice they don't have Cabinet committees yet. There's a process you go through to check unintended consequences, and I hope that they step their way through those."