Changes to the decades-old Petroleum Resources Rent Tax (PRRT), announced as part of the federal budget, already intend to claw back an extra $2.4 billion over the next four years.
But a group of crossbenchers, whose votes could be vital, are calling for a greater share of revenue for Australians from the massive fields.
Costing more than $200 billion to develop, critics say two thirds of the gas projects off the coast of Western Australia still pay almost no tax and may never be liable.
The Greens, along with independents David Pocock, Jacqui Lambie and Tammy Tyrrell, say they will pass the budget measure if the tax take becomes less modest.
Treasurer Jim Chalmers on Tuesday rejected the crossbenchers' demand to further increase the tax, which would have added an additional $2.6 billion in tax revenue over four years.
The PRRT tax applies to large offshore fields operated by Woodside, Chevron and Exxon and the proposed amendments have not yet come before parliament.
The coalition says it is yet to see the detail or draft legislation for Labor's plans to increase the tax.
"The government needs to roll back their anti-investment policies which are killing resources projects, otherwise higher taxes on fewer projects will just be a hollow achievement for Labor," coalition spokeswomen Susan McDonald told AAP.
Dr Chalmers has the support of the sector, which hopes the coalition will come on board.
Without his amendments, most of the liquefied natural gas projects are not expected to pay significant amounts of petroleum tax until the 2030s.
Australian Petroleum Production & Exploration Association chief executive Samantha McCulloch said the government's proposed tax changes provided greater certainty for future investment required for domestic and regional gas supply security.
"Bipartisan support is important because Australia needs a strong and sustainable future for the gas industry and that requires stable and enduring policy settings," she told AAP.
It is important to note the oil and gas industry contribution was growing considerably even before this extra $2.4 billion was proposed, Ms McCulloch added.
Prime Minister Anthony Albanese said the government's position was sensible and it intended to pursue it.
"The crossbenchers are only coming to play because the coalition consistently vote no to everything," he said.
The government is acting on Treasury's key recommendation to achieve a fairer return - and sooner - from offshore LNG projects by introducing a cap on the use of deductions from July 1, 2023.
The change is intended to limit the proportion of PRRT assessable income that can be offset by deductions to 90 per cent, while limiting impacts on investment incentives and risks to future supply.
The crossbenchers want that cap lowered to 80 per cent.
Greens senator Nick McKim said fossil fuel corporations needed to pay their fair share of tax.
"The gas cabal has been playing the major parties like fiddles," he said.
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