Either side is needed to get the Labor rejig of the Morrison-era stage three tax cuts through the Senate.

The Prime Minister wants "sooner the better" action to meet deadlines for the change to come into effect by the July 1 start date. It is a policy Treasury insists it began working on in December without direction from government.

The Prime Minister on Monday told the Labor caucus the tax change was an example of people over politics and "good economic policy" that will "make an enormous difference".

"You can't say that there's cost-of-living pressures on low- and middle-income earners and then refuse to do anything about it," he said.

"And what we have done is make not an easy decision. We've made a right decision at the right time for the right reasons."

Shadow cabinet, while highlighting a broken election promise "betrayal", was to come to a position before the joint parties meeting on Tuesday morning, but members had flagged it was a "short-term solution" to cost-of-living pain.

Shadow cabinet, while highlighting a broken election promise "betrayal", was to come to a position before the joint parties meeting on Tuesday morning but members had flagged it was a "short-term solution" to cost-of-living and stated concerns about bracket creep sending "aspirational" taxpayers to higher tax brackets and paying more.

Meantime, the Greens want the tax changes to be fairer to lower income earners and have proposed that the already halved tax cuts aimed at higher income earners be redistributed to those less well off.

The government expects debate on the legislation in the House over several weeks where it has the numbers to pass it, before it hits the Senate.

The Prime Minister wants it passed by Easter and has taunted the opposition for "struggling" to come up with a position for two weeks.

"This will be a debate that we're not just willing to have, but enthusiastic about having," Mr Albanese said.

"Because it is about looking after people in the finest of Labor traditions."

"That's what we do. We look after people. We look after people who need that assistance, but we also look after people's aspiration as well. And this package does both of those things."

Senior opposition members, including Finance spokeswoman Jane Hume, said the new policy was politics over people, at the same time as reiterating the Liberal party was a party of "lower, simpler taxes".

Liberal MP Bridget Archer told The Canberra Times it would be "pretty hard" to walk away from Labor's amendments that offer tax cuts for all taxpayers.

"I think it's always good not to deal yourself out of the game," Ms Archer said.

Ms Archer wants the Labor amendments passed, but noted "this is not an antidote to cost-of-living, either".

"It's very useful, but it's not the answer to cost of living, particularly when we see the level of challenge that exists in my electorate. I mean the levels of homelessness are like I've never seen before and growing," she told this masthead.

Ms Archer, who co-chairs the Parliamentary Friends of Ending Poverty with Labor MP Alicia Payne, wants to see wider relief in the May budget for people on lower incomes, including pensioners and job-seekers not paying tax.

The Greens have also indicated they are not keen on simply waving the legislation through, flagging a "couple of options" for negotiations.

"They need to fix it, not come up with solutions that leave millions of people behind," Greens leader Adam Bandt said.

"About $80 billion of the cost-of-living plan is going to the top tax bracket. That's about enough to get dental into Medicare for everyone.

"Another option is looking at whether it's better to spend $80 billion on a tax cut for the top end, while people on income support are still left to struggle with increased rents under Labor's housing crisis and get nothing at all."

The Greens and Senate crossbenchers are also considering sending the legislation to a Senate inquiry which would make an Easter deadline difficult.

"We're seeking to have discussions across the Parliament about the best way to spend such an enormous amount of money and we're considering our position," Mr Bandt said.

"The Prime Minister has to explain why he's giving Clive Palmer, Gina Rinehart and other billionaires a $4500-a-year tax cut or giving an extra $15 a week to people on middle incomes and many people get nothing at all."

Meantime, Treasury officials told a Senate committee hearing on Monday the government did not instruct the department to include tax changes in proposals it began developing in December.

Head of Treasury's revenue group Diane Brown said the department was asked to begin developing options for cost-of-living relief following a meeting between Treasurer Jim Chalmers and Treasury secretary Steven Kennedy on December 11 last year.

Ms Brown said the department had taken it upon itself to include changes to the stage three cuts as part of options to be considered in providing relief for households under financial strain.

"The secretary was very concerned that any cost-of-living relief didn't add to inflation," she said.

"Preliminary work began on a range of options but, in the end, given our objective of not having cost-of-living relief that added to inflation, we settled on the advice that was provided [to Dr Chalmers] on January 20."