Crucial Senate crossbencher Jacqi Lambie has suggested she might push for changes to the Morrison government’s flagship income tax cuts.

The coalition’s $158 billion tax package passed the lower house on Tuesday and is heading for the Senate, where the government needs the support of four-of-six crossbenchers to get it across the line.

Senator Lambie is yet to declare if she will support the full three-stage package.

But she is worried about the final stage, which doesn’t kick in until mid-2024.

“They are five or six years away and that’s a bit worrying because we don’t know where the economy’s going,” Senator Lambie told reporters in Canberra on Wednesday.

“They’re big calls. I would like to put a safety procedure in that stage three.”

The senator is not worried that amending the bill could hold up tax relief for Australians.

“I’m watching it play out, you know what politics is like. It changes more than you change your undies.”

The government is in the market for crossbench support because Labor won’t support the tax package in full.

Instead, the opposition is hoping it can convince crossbenchers to support its amendments, so that the second stage can happen sooner and the third stage can be voted on later.

Labor argues the third stage of the plan – set for 2024/25 – is too far off for the parliament to decide on now.

“This is a government which has got the economy wrong at every turn,” shadow treasurer Jim Chalmers told reporters.

“[It] now wants to pretend that they know what the economy and budget will look like in five years time.”

Treasurer Josh Frydenberg’s is piling pressure on Labor.

His latest tactic is to highlight how much the nation’s lowest-earning electorates will miss out on if the plan doesn’t pass this week.

In Victoria, the electorate with the lowest average taxable income ($60,901) is Bruce in Melbourne’s southeast, held by Labor MP Julian Hill, where the coalition says people would miss out on $15,348 over a decade.

The lowest-earning electorate in NSW is Blaxland in western Sydney ($62,057), held by Labor’s Jason Clare, where the government says people would miss out on $15,516 over 10 years.

The government is edging closer to sealing a deal on passing its full package before parliament rises.

Centre Alliance MP Rebekha Sharkie supported the bill in the lower house, but said her two senate colleagues were still negotiating with the government on ways to reduce gas prices.

Former Liberal Cory Bernardi also backs the tax relief package, leaving the government just one vote short.

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.