In a sign of the volatility of the new Senate, the Federal Government has lost a vote on one of its bills to axe the carbon tax, and seen one of its own senators cross the floor on an amendment to another.

The legislation that failed to pass would have abolished future income tax cuts brought in under the previous Labor government to compensate for increased household costs under a floating carbon price.

The tax cuts are due to come in for low income earners on July 1, 2015 and will cost the budget at least $1.5 billion over four years.

The Government argues that without the carbon tax, the tax cuts are not necessary.

But the Senate voted against the Government's legislation 40 votes to 33 with all but one of the eight crossbenchers siding with Labor and the Greens.

The three Palmer United Party (PUP) senators, Motoring Enthusiast Party senator Ricky Muir, Family First senator Bob Day, Liberal Democrat senator David Leyonhjelm and independent Nick Xenophon voted to keep the tax cuts, while Victoria's Democratic Labour Party senator John Madigan supported the Government's move to abolish it.

Senators Leyonhjelm and Day - who have agreed to vote together on most economic issues - say they have had an "early win" by "torpedoing" the legislation.

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The tax cuts were deferred indefinitely by Labor in its 2013 budget because the forecast price of carbon was due to drop.

Finance Minister Mathias Cormann says the Opposition has voted against one of its own budget measures.

"We're very pleased that the Senate is voting in favour of scrapping the carbon tax," he told the ABC.

"In relation to the $1.5 billion new hole that the Labor party has blown into the budget today obviously we will now reassess on how we can best proceed in relation to those issues from here."

He has indicated the Government will bring back the legislation.

"I've seen the Senate change its mind, often within the same day but certainly within a couple of weeks, so let's see how this continues to play out."

In a later vote on an amendment moved by Senator Xenophon, pushing for a review of the rules for setting electricity prices, Queensland LNP Senator Ian Macdonald crossed the floor to vote with the Greens and Labor.

The vote was tied and so the amendment did not go ahead.

Senator Macdonald said he voted against party lines because the amendment "was eminently sensible".

He has also issued a warning to his party not to expect him to agree to motions to gag debate - even though he supported one early on Wednesday.

Ricky Muir votes with Labor to frustrate Government

Manager of Government Business in the Senate Mitch Fifield began the sitting day by moving that the legislation to repeal the carbon tax be declared urgent - a motion that would limit debate on the bills and bring on an early vote.

"I totally support the guillotining of this debate because it has been debated so long and so often that nothing new can come out," Senator MacDonald told the ABC.

"But my general view is that, except in exceptional circumstances we should not curtail debate."

The Government bid failed after crossbencher Ricky Muir voted with Labor to continue debate.

Senators have been debating the bills since they were reintroduced on Monday - the first sitting day of the new Upper House.

However, with the repeal all but guaranteed to pass with the support of PUP senators and other key crossbenchers, the Government wanted to bring on the vote early Wednesday.

Repealing the carbon pricing scheme was a key election promise for Prime Minister Tony Abbott, but his bid to fulfil it has so far been stymied by Opposition and Greens MPs.

After Senator Fifield tried to guillotine the debate, the Leader of the Opposition in the Senate, Penny Wong, accused the Government of trying to manipulate the Senate vote to suit the Prime Minister's media schedule.

"I utterly object, as does every senator on this side, to this chamber of the Australian Parliament being used as a plaything of the Prime Minister," she told the Senate.

"What an outrage that we would have the Senate being asked to gag and guillotine legislation so Mr Abbott can do a press conference tomorrow in time for prime-time television.

"It is an absolute disgrace and really demonstrates the arrogance of this Government."

Government Leader in the Senate Eric Abetz argued there has been enough discussion about legislation, which was debated and voted against by Labor and the Greens in the previous Senate.

"This package of bills has had 33 hours and 52 minutes of debate in the Senate and according to Labor that is gagging and guillotining," he said.

Vote heralds cry of 'Onya Ricky'

Greens leader Christine Milne said the Senate could not allow the Coalition to "ram through" the repeal.

"This is probably the most important package of bills for Australia's future," she said.

Senator Xenophon issued a "plea" to his fellow crossbenchers to allow debate to continue until Thursday morning.

"This is about the Senate doing its job," he said.

The Government move was supported by PUP senators Glenn Lazarus, Jacqui Lambie and Dio Wang along with Senator Day and Senator Leyonhjelm.

But it needed one more vote from the micro-party crossbench, and the remaining three senators - Senator Muir, Senator Xenophon and Senator Madigan - all sided with the Opposition.

When the vote was held, one senator was heard to exclaim "Onya Ricky".

It is one of the first votes of the new Senate to demonstrate the flexibility in the loose agreement Senator Muir signed with PUP last October to act as a voting bloc "where it is practicable".

However, the deal has stuck in relation to voting against a multi-billion dollar budget measure to abolish the Australian Renewable Energy Agency (ARENA).

The Government announced in the budget that it would axe the $3 billion agency, which was set up under the previous Labor government to fund renewable energy projects and research.

Senator Muir and PUP have released separate media statements saying they will fight to keep the agency.

"I have been a supporter of renewable energy for a long time and I am very pleased with this outcome," the Victorian Senator said in a statement.

However, both parties say they will allow the government to go ahead with cutting the agency's budget. It announced at budget time that it would return $1.3 billion into consolidated revenue.

Debate on the bills is continuing with a vote expected today.