The federal government has suffered another blow to its beleaguered budget after being forced to retain tax-cut compensation due to start next year and an expensive energy-research agency, both of which were slated to go under its carbon-tax repeal package.

Amid growing concerns internally about its management of the new crossbench-dominated Senate, the government was first defeated on a procedural motion to force the carbon-tax repeal to an early vote on Wednesday, and then learnt it would be blocked on the proposed abolition of the Australian Renewable Energy Agency.

It also lost a vote on another critical aspect of the carbon-tax repeal when the otherwise pro-repeal Liberal Democratic Party senator David Leyonhjelm combined with the Greens, Labor and other crossbench senators to keep $1.5 billion worth of tax relief due to start from July 1 next year.

However, the government argues it had already factored in the retention of Labor's second round of tax cuts in light of the stated positions of Senator Leyonhjelm and the Palmer United Party.

The developments capped off a chaotic day in the Senate.

Australian Motoring Enthusiast Party senator Ricky Muir refused to back the carbon-tax guillotine motion even though it had been assumed his vote was aligned to the Palmer United Party, which backs the carbon-tax repeal.

The government had counted the anti-carbon tax Victorian in its own column. After first thinking it would achieve its long-held ambition to scrap the carbon tax on Wednesday, the government now expects there will be a vote to repeal the carbon tax by lunchtime on Thursday.

Finance Minister Mathias Cormann said on Thursday that he was ''hopeful'' that the carbon tax would be repealed.

''It looks like the carbon tax will be history very soon,'' he told ABC radio.

''I don’t take anything for granted until it has all happened,'' he said. ''But I'm certainly very hopeful and quietly confident that the carbon tax will soon be history.''

On Thursday morning, Prime Minister Tony Abbott said he maintained confidence in his Senate leadership team, led by Eric Abetz, despite the crossbench blowing a more than $9 billion hole in the budget by refusing to pass savings measures associated with the repeal of the carbon and mining taxes.

"I have great confidence in the ability of all of my frontbench and the Senate leadership team," Mr Abbott said. "In the end, though, this is a question of keeping commitments. The Coalition committed to scrap the carbon tax. Just about all of the crossbench senators committed to scrap the carbon tax, so this is a day for people to keep their commitments."

Senator Muir, the notional fourth senator in the PUP bloc, had proposed his own amendment to the carbon-tax repeal package to save ARENA.

In a last-minute deal with Palmer United Party leader Clive Palmer, the amendment, which would have further delayed the carbon-tax repeal, was withdrawn in exchange for PUP's support for keeping ARENA alive, albeit with reduced funding in the short term.

The news was a big setback for the government, which this week alone has been rebuffed over some $10 billion in savings it had already booked in its budget projections from scrapping the mining and carbon taxes and a range of spending programs connected to them.

Funding will be necessary to finance a lift in the tax-free threshold from $18,200 to $19,400, and more is needed to keep ARENA going. There are also additional costs associated with retaining the Climate Change Authority, the Clean Energy Finance Corporation and the Renewable Energy Target, all of which it had hoped to dump in exchange for its Direct Action policy.

Mr Palmer attempted to explain the outcome by suggesting it had been his preference all along.

''We have decided to support the government's plans to reschedule the agency's funding,'' he said.

''I had extensive discussion with former US vice-president Al Gore about ARENA and was convinced by his arguments in support of this important agency.''

As a result, the carbon-tax repeal will cut the ARENA's budget by $435 million and will enact a previously announced deferral of $370 million in funding by the former Labor government.

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