Labor and the Greens will split the Coalition’s package of legislation repealing the carbon tax to try to “save” the independent Climate Change Authority and the $10bn “green bank” which is making a profit while financing clean energy loans.

Both Labor and the Greens still intend to use their Senate numbers to vote down the repeal of the tax and oppose the abolition of the two bodies – the Climate Change Authority and the Clean Energy Finance Corporation – meaning the fate of the 11 government bills is likely to fall to the new Senate which sits from July.

But they will use the tactic of separating the fate of the two institutions from the repeal of the carbon pricing scheme to highlight their view that both are still necessary and useful even under the Coalition’s plan to achieve greenhouse gas abatement through “direct action”, primarily competitive government grants.

Labor’s Senate leader, Penny Wong, said the future of the two organisations should be separate “because they are of such importance” and claimed the government was trying to debate the 11 bills together “to limit debate, scrutiny and consideration”.

The Greens leader, Christine Milne, said the move gave the prime minister, Tony Abbott, a “chance to show that he is not driven by pure ideology on global warming. We are giving him an opportunity to do the right thing on the CEFC and Climate Change Authority … We want to test the Abbott government’s rationale for abolishing them separately from the price on pollution.”

But the leader of the government in the Senate, Eric Abetz, said the move was “breathtaking” in its “economic stupidity” and an example of an opposition “trying to delay the inevitable”.

The parliamentary move comes as the Coalition tried to shift attention from its policy changes on schools funding back onto the Senate vote on the carbon repeal laws, due before parliament rises for the Christmas break.

Abbott took to YouTube to deliver his message, telling families “You could do a lot with $550, that’s what every Australian household will get from the abolition of the carbon tax” and calling on the Labor leader, Bill Shorten, to give Australians “the best possible Christmas present”.

The report from a quick Senate inquiry into the carbon tax repeal was expected to be split along party lines.

The Climate Change Authority, chaired by the former Reserve Bank governor Bernie Fraser, delivers independent advice about how well greenhouse gas policies are working, what Australia’s reduction target should be and what risks climate change poses. The Abbott government intends to abolish it and rely on advice from reviews by the Department of Environment if they are commissioned by the environment minister.

The government rejected advice in the authority’s interim report in October which said Australia’s 5% emissions reduction target for 2020 is “not a credible option” and should be increased, possibly to 15% or 25%.

Wong said the abolition of the authority was an example of those who deny climate science trying to avoid discussion and information about what it would mean for the future.

The Coalition derides the CEFC as the “Bob Brown bank” and says closing it will save money, but the CEFC says it will actually generate a positive return for the government .

At a Senate inquiry hearing last week the CEFC chairwoman, Jillian Broadbent, and its chief executive, Oliver Yates, insisted scrapping the organisation would cost up to $200m annually in lost revenues. “It will cost the taxpayer more to shut down the CEFC than it will save,” Broadbent said.

Wong said this revelation showed the Coalition was being “blindly ideological” and demonstrated why it was so important to debate the future of the CEFC.

The Coalition could return the bills to the Senate next year, when a second rejection would give them a trigger to call a double dissolution election, but it would be unlikely to call such a poll before attempting to pass the bills through the new Senate, where the balance of power will be held by Palmer United party senators and the Motoring Enthusiast party senator who has vowed to join the PUP in a voting bloc.

The PUP founder, Clive Palmer, has refused to reveal how his senators will vote, but has insisted any repeal should be “retrospective” – wiping the carbon tax bills of liable companies. That would include the $6.17m in unpaid carbon tax owed by his company, Queensland Nickel.