The Greens and Te Pāti Māori are warning Labour that ruling out capital gains or wealth taxes could threaten their chances of a coalition deal.
National and ACT also say the promise is premature, and likely to be overridden.
Alongside the release of Budget documents today, Labour leader Chris Hipkins admitted he had shut down plans for a "tax switch" in this year's Budget, which would have seen a tax-free bracket and a 1.5 percent tax on wealth above $5 million from 2024.
But he also went a step further, ruling out introducing any wealth tax or capital gains tax "under a government I lead", an echo of a similar pledge from his predecessor Jacinda Ardern.
This conflicts with the priorities of the Green Party - who, polling has consistently showed, Labour would need to form a government.
Their policy - the first they announced this election - would to introduce an "income guarantee" of a tax-free bracket for all earnings under $10,000, funded by a new tax bracket of 45 percent on income over $180,000, and a 2.5 percent wealth tax on assets.
Labour would also likely need Te Pāti Māori, which has also spoken about plans to "tax the rich" as part of its election campaign this year.
Both parties came out swinging, with the Greens' co-leader James Shaw telling reporters it was disappointing, and Labour had "got it wrong".
He said there was a "very real possibility" the Greens would not work with Labour as a result.
"It does depend on how many MPs we've got, and it does depend on the rest of the agreement - but we have always maintained the option of just sitting on the cross-benches ... I think that there is a very real possibility of that," he said.
"This is a priority for us, it has been a priority of ours for some time.
"I don't think any political party leader can categorically rule out what the agenda of the next government is under MMP - that is ultimately for voters to decide."
Shaw said the government had done "quite a good job" in lifting about 30,000 children above the material hardship line, but about 45,000 were still below it.
"I feel very strongly about this, and the Greens have campaigned for a progressive tax system for a very long time. We have said a number of times that poverty is a political choice.
"We're a wealthy country, we have the ability to end poverty here. And ending poverty enables us to do more things as a country as well."
In an earlier statement, he said governments had been tinkering on the edges of the tax system for too long, and "the time for tinkering is over, the time for political courage is now".
"Governments have been tinkering at the edges - constrained by self-imposed refusal to tax the wealthy - instead of taking the bold decisions people need right now. If political leaders are not willing to take those decisions on behalf of the people of the country you purport to lead, then why be in politics at all?"
He thought Hipkins was a very principled politician with a deep commitment to public services and education, but "I don't think that there's any point in political power if you choose to do nothing with it".
Te Pāti Māori co-leader Debbie Ngarewa-Packer was similarly scathing, saying for all Hipkins' talk of "bread and butter" it was those struggling to put bread and butter on the table who would lose out.
"He is more concerned about winning voters who would be upset by any disruption to what they've seen be the norm, and I guess there has been a real ignorance and a normalisation of poverty as long as it's not in your backyard. And that's the status quo," she said.
"The tax system is currently designed for the rich and it's got to stop. We've got to bring a balance back into our nation. Our nation and our people deserve it."
She said Hipkins was "arrogantly" saying he did not want to do business with either of the left-leaning minor parties.
"Whether it be the Greens or Te Pāti Māori, effectively saying he's not open for business or negotiations, and I think that's really unwise.
"Elderly can't afford their food, families are working three jobs, we can't afford to be a nation that continues like that.
"If you're not going to tax the rich, if you're not going to tax the houses, take GST off food, capital gains tax, then what are you doing? Basically you're doing nothing, so what would we have to discuss?"
She said he did not really have the option of doing that.
"I don't think the prime minister - or the polls - is in a position, to state what he would absolutely not do ... he does not have the luxury to dictate how and what he will or won't do to stop poverty."
She stopped short of completely ruling out working with Labour if such a tax were not up for negotiation, however.
"We've always been open and honest about what it is that we require in a relationship, and that would be our values decision," she said.
"They shouldn't be and he shouldn't be so callous as to sit there and say 'I'm wanting to make whānau live well and be well, but actually I'm not open to any transformational change to achieve that.
"If he takes it off the table, what in hell is he proposing to rebalance and address pain and poverty in Aotearoa?"
National and ACT question Hipkins' sincerity
Hipkins attacked National's long-proposed tax cuts by as "unaffordable and inflationary".
"Just as we are getting on top of price increases, they would borrow to deliver an inflationary sugar hit. National's uncosted and unfair tax changes would deliver the biggest cuts to millionaires and CEOs while offering while offering as little as $2 a week to some low and middle income households.
"Some people might call it boring, but the times call for restraint and simple and smart policies which grow our economy, help drive inflation down and provide targeted help to those families who need it the most."
National's leader Christopher Luxon suggested Hipkins' promise was a bluff, calling it was a desperate political move that showed Labour could not be trusted.
"It's very hard to work out what Chris Hipkins stands for anymore," he said. "He knows it's unpopular, it's been unpopular. Unlike the previous prime minister Jacinda Ardern he refused to rule it out as leader and as prime minister.
"I've asked him many times in Parliament would he rule it out, he said no. And yet we now have a situation where it's the coalition of chaos, we have Labour saying they're ruling it out for real this time but who knows, and we've got the Green Party saying it's desperately part of a coalition agreement.
"I tell you what's going to happen, they will bend to the coalition of chaos partners of the Green Party and Te Pāti Māori."
He refused to say whether bringing in a "tax switch" would be justified, instead referring to the government's increased spending and National's policy.
"All we're going to do is take the tax thresholds and lift them up by inflation so that actually just like beneficiaries, just like minimum wage workers, just like pensioners, they actually get tax relief because it's inflation-adjusted tax relief."
He said National's approach would be simpler than the proposal put forward by the Greens - but National has not yet put out costed tax policy explaining how its cuts would be paid for.
Luxon said a wealth tax would have "destroyed and put a wrecking ball through the New Zealand economy", saying with the economy in recession it was not the time to introduce new taxes.
ACT leader David Seymour told RNZ the Greens and Te Pāti Māori would team up with proponents in Labour to force Hipkins to introduce a capital gains tax.
"I think the government doth protest too much - they've been asked to rule out a capital gains tax so many times, they've refused to do it until now. They've revealed they were looking into it only a few months ago.
"What we know for sure is their only path to power is dependent on ... the Māori Party and the Greens who might not even bother with taxation, they'd rather go straight to looting anybody who's got two pennies to rub together.
"Chris Hipkins is the last man standing against the capital gains tax and even he only stands there as a matter of political convenience."
If Hipkins was prime minister after the election, he would have to face down revenue and finance ministers who were in favour of a tax, his coalition partners, "and apparently his own conscience", Seymour said. Hipkins has previously expressed support for a CGT.