They don't like sole parents, in particular, being "paid to breed" by having more children after going on the benefit. But nor do they want to harm their children.
"If they have more than one and they are not married, castrate them," says an 85-year-old woman at Auckland's Avondale market.
But then she adds quickly: "That's being a bit facetious. I don't know, it's hard where children are concerned."
A welfare working group led by economist Paula Rebstock recommended this year that sole parents and partners of other beneficiaries should have to look for part-time work when their youngest children turn 3, and fulltime work when their children turn 6.
A majority also wanted to make women who have another baby after going on the benefit go back to work after 14 weeks.
The National Party appears to have read the public mood when it announced last week that it would make sole parents look for part-time work only when their youngest children turn 5, and fulltime work when children reach 14 - the age at which they can legally be left alone.
But it is less clear whether voters will support another part of the policy that would make women who have another baby after going on the benefit look for paid work again after one year.
Only 12 per cent believe sole parents should look for work before their children turn 5. Half (49 per cent) support a work test when the children turn 5 or 6, another 20 per cent think the work test should start at various ages between 7 and 17, 4 per cent say it depends on the children's health or other factors, and 15 per cent would not force sole parents back to work at all until their children turn 18.
Devonport salesman Grant Cowling, 47, would push them to work when their children turn 2 because he feels the benefit is being abused.
"I have family members that have had eight children ... with four different fathers, because she chose to. You can do that in New Zealand, you can have a reasonable life on the DPB," he says.
"I think they are going to have to take a hard line and say, 'No, after the second child your family has to take responsibility."'
Takanini kiwifruit packhouse manager Colin Davis, 32, believes sole parents should look for work when their children reach 3, with subsidised childcare. "I'm not a total fan of welfare because it creates some bad habits, but I believe in having welfare for people who need it," he says.
Christchurch caregiver Yvette Kinley, 57, has a daughter who is a working solo mum who finds it tough juggling work and children. She says sole parents should look for paid work when their children turn 6 or 7.
"I think it should be part-time work," she says. "Sometimes when they are teenagers they need their parents more."
Hannah Styles, a fulltime homemaker of Reporoa, is against forcing sole parents to work in principle.
"I think it's important that parents are home with their children, or at least one parent is," she says. "What's the point of having a child if you are not going to be at home with them?"
Asked about the welfare system in general, many people suggest tightening it. Some say people should work for their benefits, others suggest American-style food stamps or time-limited benefits.
"I reckon the dole should be only for six months. If there are no jobs, you can move. We have to," says Te Aroha sharemilker Lindsay Burgess, 42.
And 79 per cent reject Dr Morgan's proposed $11,000 basic income for everyone, because it would encourage some not to work and because it would be too harsh for sole parents, who now get at least $19,600 including family tax credits, and superannuitants, who get $17,700 if living alone.
Only 15 per cent support the idea and 5 per cent agree in part. "You'd be taking from people what they are entitled to, to give to other people who might not need it," says Devonport doctor Amanda Jones.