Low and middle-income earners will pocket more than $1000 after the Morrison government passed its full package of tax cuts.

Prime Minister Scott Morrison has hailed the government’s victory as a win for Australians.

“These are the people we will keep our faith with every single day,” he told reporters in Canberra.

“I said we would burn for them and that is exactly what we’ve been doing this week.”

The first stage of the plan will deliver up to $1080 to low and middle-income earners when they lodge their tax returns in coming months.

The second stage will top up a low-income tax offset, which means more people – earning up to $45,000 instead of $41,000 – will get a 19 per cent tax rate.

The final stage flattens the tax rate from 32.5 per cent to 30 per cent for people earning between $45,000 and $200,000 from mid-2024.

Mr Morrison dismissed Labor’s claim that future tax relief would make cuts to services inevitable.

“Our plan was independently verified by the secretaries of finance and treasury at the election. It doesn’t get any more certain than that,” the prime minister said.

Labor unsuccessfully tried to scrap the third stage and bring the second stage forward before voting for the bill, which cleared the upper house 56 votes to nine.

The opposition will review its position on the final stage closer to the next election.

Labor Leader Anthony Albanese was at pains to point out this did not necessarily mean repealing the third tranche.

“I haven’t said that at all,” he told the Nine Network on Friday.

Tasmanian independent Jacqui Lambie lobbied for her state’s $157 million public housing debt to be erased or renegotiated in return for her support.

Chief negotiator and Finance Minister Mathias Cormann told parliament he would work through the issue over the next six to eight weeks, but stopped short of any solid commitment to wipe the debt.

Centre Alliance initially boasted about securing a deal which would lower gas prices, before being forced to admit the guarantee amounted to a “draft policy”.

Senator Cormann indicated he would continue to look at measures around gas, although he rejected suggestions of a “special deal” with the minor party.