"Petrol rose $1 [a litre] in just 12 months," he said. "I was speaking to kiwifruit workers, they said covering the cost of getting to work for a week already swallowed a day's wages."
Government officials previously estimated the cost to employers of lifting the minimum wage to a living wage at $1.3 billion, or $930 million after the April 1 increase.
"However given so many employers have increased wages recently it would likely be significantly lower," Miller said.
The Fairer Futures group also wants core benefits to be lifted, sanctions to be removed, and welfare to be individualised - rather than penalising beneficiaries who get into a relationship.
A report in March showed that even after increases in April, benefits needed to be raised by up to $165 a week for some households just to cover basic costs, or $300 to meet the total costs of participating in society.
"While some families are feeling the pinch, others are barely clinging on," said Glenis Philip-Barbara, Assistant Māori Commissioner for Children.
"Mokopuna we have spoken to say they just want enough to cover the basics, and a little bit more."
Fairer Futures wanted all debt to the Ministry of Social Development - estimated at around $1.9 billion - to be wiped. The Herald previously reported that much of this debt was owed by families who were overpaid in tax credits after they failed to tell MSD that their family circumstances had changed. Those Working for Families overpayments were then treated as debt and interest was often charged.
Marcela Mingoti, finance manager at Nga Tangata Microfinance, said an analysis of their clients last year found that their average income was $36,000, their debt was $13,000 and they owed an average of $3064 to MSD.
She shared the budget of one of her typical clients, Mary*, a single mother with three children.
"Despite being entitled to Working for Families credit, Support Living Payment and Child Disability Allowance, her fortnightly gross income is only a little over $760.
"After the advances payments are deducted from her benefit, she is left with $574 to support her family of four for two weeks.
"A quarter of her income is allocated to pay government debt. I wonder how Mary would be able to feed and house her family without getting trapped in a loan to cover her basic needs. She will not. That's why she came to us - she had a high-interest debt that wasn't being addressed and was incurring extra charges."
Mingoti said some clients paid a "symbolic" amount of $1 or $2 a week towards their government debts, meaning it would take between 58 and 116 years to pay them off.
"Realistically, this debt is uncollectable."
Prime Minister Jacinda Ardern acknowledged last month that increases to benefits and other support in April did not go far enough.
Ardern said the changes were part of a policy platform that had made New Zealand a better place than it was when she took office four years ago; fewer children were going hungry at school, thanks to school lunches policies, benefits had been increased and indexed to wages, and incomes overall were up.
THE ANTI-POVERTY BUDGET CHECKLIST
• Increase core benefits to standard of liveable incomes
• Raise minimum wage to living wage
• Increase the disability allowance
• Overhaul the relationship rules for beneficiaries
• Remove benefits sanctions
• Wipe debt owed to MSD
• Improve supplementary assistance and urgent grants
*name changed for privacy purposes