Rudd, Gillard and party heavyweights deny the possibility.
But Abbott has been targeting Gillard mercilessly and trying to bring about her downfall and a snap election that all polls show the Opposition would win by a landslide.
The latest is a quarterly analysis of Newspoll results, published in the Australian yesterday, which showed Labor was now trailing the Coalition in all mainland states, and that if an election was held now it would lose half its seats in New South Wales and all MPs but Rudd in Queensland.
Gillard has also lost the support of the nation's female voters.
After last year's election she led Abbott as preferred prime minister among women voters by 52 per cent to 33 per cent, the Australian said.
By the end of last year, Gillard had pushed her lead out to 55 per cent to 29 per cent - but in the past three months her support among women as preferred prime minister fell from 47 per cent to 39 per cent.
In contrast, Abbott's backing among women has risen from 33 per cent to 37 per cent, making the two close to equal.
Women voters' satisfaction with Gillard has also plummeted from a post-election high of 45 per cent to 30 per cent.
The Australian said satisfaction with Abbott among female voters was 35 per cent and dissatisfaction was 54 per cent.
Abbott was now the preferred prime minister in every state except Victoria and led Gillard for the first time in NSW, South Australia, Western Australia, in regional areas and among older voters.
More grim tidings came yesterday with the release of this year's Mapping Social Cohesion survey, written by Professor Andrew Markus of Monash University, which prodded two of Gillard's most vulnerable - and painful - sore points.
While Gillard is struggling to form a cohesive policy on asylum seekers in the wake of the High Court ban on her planned refugee-swap deal with Malaysia, the survey showed strong support for Abbott's hard line.
More than one-third of respondents said boats carrying asylum seekers from Indonesia should be turned back at sea, or their passengers locked up until they could be deported.
And her loose alliance with the Greens, whose support is crucial to her survival, appears to be at odds with the feelings of many voters, including Labor supporters.
The survey found that Labor voters were much closer to Opposition supporters than they were to the Greens on a range of issues.
About one-third of Green voters placed the environment, climate change and water as the most pressing problem facing the nation, compared with just 15 per cent of Labor and 6 per cent of Coalition supporters.
But for both leaders the survey held one key message: their constituents are losing faith in politics and politicians.
In the past two years the number of people who trusted the federal Government had dived from 48 per cent to 30 per cent, spilling over into attitudes towards other parts of the community.
People trust each other less, and fewer are involved in voluntary work.
