SUPPORT for the Labor government has fallen to 27 per cent, its lowest point in almost four decades, while Julia Gillard's personal ratings have collapsed to levels not seen for a prime minister since John Howard introduced the GST more than 10 years ago.

The latest Herald/Nielsen poll also shows that a week away from the first anniversary on June 24 of Kevin Rudd's dumping as prime minister, twice as many voters prefer Mr Rudd as Labor leader to Ms Gillard.

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The poll, taken from Tuesday to Thursday night, contains a sliver of good news for Labor in that support for putting a price on carbon has jumped 4 percentage points in a month to 38 per cent.

But the government is in dire straits. A little more than one in four voters would choose Labor first should an election be held today, and almost 60 per cent disapprove of Ms Gillard's performance.