Treasurer Jim Chalmers has urged opposition parties to get behind the government’s amended tax cuts to help Australians struggling with cost of living.

Chalmers will introduce legislation for the revised tax cuts when parliament resumes on Tuesday and said it was time other political parties came to a position.

“I say to the Coalition and to the Greens: Don’t stand in the way of a bigger tax cut for more workers to help with the cost of living,” he told ABC on Monday.

The revamped tax package was high on the agenda at a Labor partyroom meeting on Monday, while the Coalition is yet to say whether it will back the plan.

The government needs the support of the Coalition or the Greens and two crossbenchers for its changes to pass the Parliament. On Monday, independent senator Jacqui Lambie signalled her support.

Lambie praised Prime Minister Anthony Albanese for “having the courage” to revise the already-legislated tax cuts as economic circumstances changed.

“I don’t see that as a lie. I see that as common sense and those people that need it most in society … we’re going to pass some down to you. And so we should [because] that is the Australian way,” she told Nine’s Today show.

She urged the Coalition to support the changes because otherwise “you’re going to let the Greens start negotiating”.

“I think it’s common sense by the Liberal Party to support them and knock the Greens clean out of the game,” she said.

Opposition finance spokeswoman Jane Hume said the Liberal Party would always back lower taxes.

“When you keep bracket creep in your tax system, you are robbing your future prosperity,” she said in Canberra.

Asked if he would support a short Senate inquiry into the changes, Chalmers said the impacts of the proposal were already well known.

“People know that there are cost‑of‑living pressures in our community … this is an important opportunity to do the right thing by people who are doing it tough,” he told ABC News.

Treasury officials told a Senate cost-of-living inquiry on Monday the government asked them to look into possible changes to income tax in mid-December.

The changes were then presented to cabinet in late January.

Treasury’s deputy secretary for revenue group Diane Brown told the committee on Monday that Treasury secretary Steven Kennedy had been “thinking about how to provide cost-of-living relief in a way that didn’t add to inflationary pressures”, she said.

“He was interested and had mentioned to us around roughly the same time that he would like the department to think about whether adjusting the personal income tax rates and thresholds could provide broad-based relief to all taxpayers in a way that didn’t add inflation,” she said.

“We were concerned that bracket creep would still be returned and so the envelope for returning bracket creep was roughly the same.”

Ahead of changes to the previous government’s tax plan, Labor had maintained it would not alter the package.

With most of the focus of the amended plan has been on short-term winners and losers, the Grattan Institute has investigated the impact of Labor’s tax package over 10 years.

The policy think tank found taxpayers earning about $68,000 a year would pay $8040 less over the period compared to the originally legislated stage-three tax cuts.

Those who jump into the next tax bracket due to wage rises – otherwise known as bracket creep – would still end up paying less.

The top 10 per cent of income earners on salaries above $130,000 were projected to pay at least $22,800 more over the decade than under the original plan, with the wealthiest workers to part with up to $45,000 more.

Under Labor’s changes, a person earning a wage of $73,000 will get a tax cut of more than $1500 a year.

At the upper end, the tax cuts for those earning $200,000 will be slashed from $9075 to $4500.

All 13.6 million taxpayers will pay less under the changes and low and middle-income earners will get a bigger cut than promised under the original scheme, although the benefit for those on the highest incomes will be pruned back.

Over the next 10 years, an average Australian on $73,000 would save more than $21,600 in tax due to the changes, analysis from the treasurer’s office shows.

But the biggest loser of the revised tax plan could be the federal budget with a $20 billion a year hit to the bottom line, the Grattan Institute warned.

-with AAP