Low and middle income earners have been guaranteed extra relief, with bipartisan support secured for changes to income tax cuts.
Opposition Leader Peter Dutton said he would not stand in the way of those doing it tough and in need of tax relief.
"We're supporting this change not to support the prime minister's lie but to support those families who need help now," he told reporters on Tuesday.
The coalition has consistently condemned the Labor government for breaking its election promise to leave the cuts untouched.
Mr Dutton said the opposition would take a significant policy to reduce taxes for Australians to the next election.
Coalition MPs and senators discussed the tax changes during a partyroom meeting, with four or five people putting forward suggested amendments and one arguing against accepting Labor's plans.
Scott Morrison, an architect of stage three tax cuts, defended his original proposal but endorsed backing the reworked package.
The coalition will refer the legislation to a Senate committee before it passes parliament.
Treasurer Jim Chalmers introduced laws backing the broader stage three package to the House of Representatives during the first sitting day of the year.
Dr Chalmers said the changes would mean more tax relief for more people.
"It's about recognising that aspiration in this country is not and should not be limited to people who are already doing pretty well. Middle Australia is aspirational Australia," he told parliament.
"This is good for workers and it's good for our economy. This is not relief or reform, this is relief and reform, more relief for middle Australia and a better reform for our economy."
Prime Minister Anthony Albanese wants the tax cuts legislated by Easter, before they take effect in July.
He told parliament the decision to change the stage three tax cuts was the correct move.
"We knew that there would be pushback ... but we knew that it was the right thing to do," he said.
"You can't say that there are cost of living pressures out there on middle Australia and then not be prepared to do everything that can do to make a difference, we will make a difference."
He and the treasurer have insisted the tax cuts will not impact inflation.
"Tax relief rolls out over the course of the year, not in a single payment, so its effect is staggered," Dr Chalmers said.
"It begins to flow from the middle of the year when inflation is expected to moderate further."
Reserve Bank governor Michele Bullock confirmed the reworked package would not materially alter the central bank's expectations for inflation or other economic forecasts.
"The bottom line really is that the fiscal envelope is the same, it's the same amount of money being handed to households but distributed slightly differently," Ms Bullock said in a news conference after the February cash rate meeting.
Under the revised package, people earning less than $150,000 will receive a greater tax cut, while those earning above that amount will still receive benefits but less than previously forecast.
Dr Chalmers said while the opposition has agreed to back in the tax cut changes, the coalition's stance had been vague.
"The opposition don't like our changes because they would prefer wages to be lower and inflation to be higher and they want tax cuts to be skewed to the highest incomes," he said.
"Their position has been indefensible, unintelligible, incoherent and unsustainable."
Economic analysis shows electorates held by Nationals MPs would gain most from the altered policy.
Findings released by the Australia Institute reveal voters in Nationals-held electorates would receive a $326 cut annually, while those in Liberal seats would be $226 better off.
Voters in electorates held by the government would receive an extra $229 per person.
