This was probably not the best week for Prime Minister Julia Gillard and partner Tim Mathieson to be told to leave The Lodge, the Canberra home for the nation's leaders for the past 82 years.

While the move to a yet-to-be-declared substitute is all about renovation rather than politics, the announcement yesterday of the first couple's imminent departure overlaps continuing leadership speculation.

The Lodge has been declared a fire threat, is contaminated with asbestos and the plumbing, roof and electrics will take months and millions of dollars to put right.

A short drive away, Parliament House is looking just as toxic in political terms. Gillard is facing votes on two crucial policies this week: her proposed carbon tax, which she is likely to win with the help of independent MPs and the Greens, and changes to the Migration Act, which could see the first Lower House defeat for a Government since 1929.

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While a Newspoll in the Australian yesterday showed Labor's primary vote up three percentage points from its record 26 per cent low, Opposition leader Tony Abbott remains the nation's preferred prime minister and would easily win an election.

Worse for Gillard was a major swing in voter sentiment on key issues. The Opposition leads on climate change, economic management, asylum seekers and national security, runs neck-and-neck on health and education, and is narrowing the gap on industrial relations.

Gillard is pushing ahead with the carbon tax and should win the vote expected today - but it will cement a tax rejected by most voters as probably the most inflammatory issue at the next election.

Debate has continued with contradictory reports from two parliamentary committees, claims from coal producers the tax will wipe out 17 per cent of the nation's coal mines and 21,000 jobs, and furious political exchanges.

Tomorrow Gillard's asylum seeker policy hangs on the independents, who will determine whether her proposed changes to the Migration Act will survive the House and allow her at least some form of moral victory when they are voted down in the Senate by the Opposition and the Greens.

Greens MP Adam Bandt and Tasmanian Independent Andrew Wilkie will oppose amendments designed to override the High Court's ban on Gillard's refugee-swap deal with Malaysia, under which 800 asylum seekers from Australia would be exchanged for 4000 United Nations-accredited refugees.

The ban is held by legal advice to apply also to the former "Pacific solution" options of Nauru and Manus Island in Papua New Guinea.

Gillard's amendments would give the Government of the day the legal power to establish detention centres or sign Malaysia-style agreements, ensuring that asylum seekers are processed abroad with no access to the Australian legal system.

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Although supported by most Australians, offshore processing is opposed by the Greens, lawyers, human rights and refugee advocates and church and social organisations. It has also been condemned by the United Nations.

The Opposition supports offshore processing, but will vote against the amendments on the grounds that Malaysia is not a signatory to UN refugee conventions.

For Gillard, success will depend on her ability to swing independents Rod Oakeshott, Bob Katter and Tony Crook to her side, an outcome that yesterday remained far from certain.

Gillard also continues to face speculation of a leadership coup, although Brisbane Labor MP Graham Perrett, who clings to one of the nation's most marginal seats, has warned he will quit if she is ousted. Labor could not win the ensuing byelection, effectively killing the Government.

New Zealand-born Labor MP Craig Thompson, meanwhile, continues to threaten Gillard's survival.

Under investigation by Victorian police over the use of an official credit card to hire prostitutes when he was national secretary of the Heath Services Union, Thompson appears to be in further trouble.

The Herald Sun reported that New South Wales police had confirmed he had been given a credit card by a company contracted by the union, which if confirmed could lead to allegations of receiving an inducement.

If convicted Thompson could be forced from Parliament, bringing down the Government.