Both Labour and the Greens are opposed to the tax cuts in the Budget, but are cautiously welcoming the benefits some families would get through a boost to Working for Families and accommodation subsidies.
A $2 billion per year families income package is the centrepiece of the government's election-year budget.
Even with that, however, Finance Minister Steven Joyce admitted about 100,000 people would remain under severe housing stress.
That was defined as having less than $180 a week left over after housing costs.
The House is sitting under urgency to pass the package into law, which Labour will oppose and the Greens and New Zealand First will support.
Labour finance spokesperson Grant Robertson said, on its own, the accommodation supplement was an "ambulance at the bottom of the cliff".
"If we're not building more affordable houses, if we're not building more state houses... there is a housing crisis."
Mr Robertson said voting for the package would be an endorsement of $1.5 billion of unfair tax cuts.
Greens co-leader James Shaw said his party supported higher accommodation subsidies.
But he said that without a significant house building programme, that could drive rents up and put further pressure on the housing market.
"You're basically taking taxpayer money and putting it into the pockets of private landlords and motel owners who are putting up emergency accommodation and so on."
Meanwhile, Labour leader Andrew Little conceded the budget was "clever politically," but said it was spin to suggest it was targeted at low and middle income families.
He hoped it would spark a debate about the country's priorities, he said.
"Being politically clever and what might go down as scoring a few points in the Wellington beltway is one thing. Building a future for all New Zealanders, a better future than we've got now, is another thing entirely."
Mr Little said he did not believe the budget was creeping into Labour's traditional territory.
"You look at the extra money that's gone into health - doesn't keep up with population growth and demographic change.
"The money that goes into education isn't enough to keep up with inflation and the demands on that sector.
"There is no new money going into regional initiatives, regional investment, job generating activities."