By Andrew Brown and Tess Ikonomou in Canberra

With most Australians expected to win out from the government’s amended tax cuts, the treasurer has warned other parties not to block the policy in parliament.

Anthony Albanese is heaping pressure on the coalition to back tax cut changes, which have received broad public support and will soon be introduced to parliament.

The prime minister said he was prepared for the political fight, with the coalition yet to confirm whether it would support the amendments.

The legislation will be introduced to the lower house when parliament returns on Tuesday.

“We’ll have debate on it in the House of Reps over the next couple of weeks, and then we’ll debate it in the Senate,” Mr Albanese told a Labor caucus meeting on Monday.

“But this will be a debate that we’re not just willing to have, but enthusiastic about having, because it is about looking after people.”

While the coalition has not yet announced its position, Mr Albanese said he would not be surprised if the Liberal and National parties rejected the tax package.

“The opposition don’t want people to have these tax cuts, and they, in their hearts, want to take it away,” the prime minister said.

“We’ll see what they decide, if they’re fair dinkum with their rhetoric, that is precisely what they will do.”

Almost two in three voters backed the changes in the latest Newspoll and the policy shift had no impact on support for the major parties.

Most workers are expected to benefit from the revised proposal over the next decade, with those earning under $150,000 to get a larger tax cut.

Treasurer Jim Chalmers pushed back against a parliamentary inquiry into the tax cuts, saying the impacts were already known.

“This is an important opportunity to do the right thing by people who are doing it tough,” he said.

Treasury officials told a cost-of-living inquiry they were asked by the government to look into changes to income tax in mid-December.

The changes were presented to cabinet in late January.

Greens leader Adam Bandt said the party was considering joining other crossbenchers in calling for an inquiry into the amended package.

Pressure applied by the Greens had previously worked in getting changes made to draft legislation, he said.

With most of the focus 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.

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 told reporters in Canberra.