The federal government’s $158 billion tax cuts are likely to come down to winning Jacqui Lambie’s support as Labor remains at loggerheads with the Morrison government over the package.

The returning Tasmanian senator is yet to declare her hand but her support is vital for the government, as it needs four out of six crossbenchers to get the three-stage plan through the upper house.

Former Liberal Cory Bernardi is the only crossbencher to have resolutely backed the full package, while minor party Centre Alliance – which has two votes – doesn’t see any “road blocks” to negotiations that could earn its support for the tax relief.

The Morrison government will introduce the legislation to the lower house when parliament resumes on Tuesday.

Labor is sticking by its refusal to back the full plan, with the caucus on Monday endorsing the shadow cabinet’s position.

It is offering to support extra tax relief only if the second stage of the package is brought forward and the third stage is shelved.

“We’re arguing a case, we think it’s a strong case,” Labor leader Anthony Albanese told reporters in Canberra.

“I haven’t given up on the government seeing common sense yet.”

Mr Albanese is concerned stage three of the plan – estimated to cost $95 billion – will permanently reduce the amount of help the government is able to provide the public.

Labor will seek to move amendments in the lower house and Senate in line with its position.

While the amendments will fail in the lower house, it is possible Labor can get enough support in the Senate to pass them.

It would then be up to the government to accept or reject the Senate’s amendments.

Finance Minister Mathias Cormann insists the government is sticking to its plan.

“We will not split the income tax relief package,” he told reporters.

“It’s a plan that we put to the Australian people, it’s a plan that was endorsed by the Australian people and it’s a plan that’s in our national interest.”

One Nation and the Greens don’t support the plan, but Centre Alliance is negotiating with the government on measures to reduce gas prices so the tax relief isn’t chewed up by rising power bills.

“We’ve still got a few things to nut out with the government … but I don’t see any road blocks,” Centre Alliance senator Rex Patrick told ABC’s AM.

“Presuming we can get an assurance that we can get energy prices down, I think we’re basically in a position where we’ll end up supporting it.”

The first stage of the plan will deliver up to $1080 to low and middle-income earners when they lodge their tax returns in the 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 will flatten the tax rate from 32.5 per cent to 30 per cent for people earning between $45,000 and $200,000 from mid-2024.

Among Labor’s concerns about the third stage is that it will be unaffordable for the budget in five years time.

Shadow treasurer Jim Chalmers says the government should accept Labor’s position and deliver a tax cut to Australians this term.

“If we want to get serious about boosting this floundering economy, we need to do something about it, and Labor is proposing a constructive way forward,” he told reporters.