One-quarter of those who prefer Rudd do not want another challenge at this stage.
An early leadership spill is unlikely, given both doubts over the support Rudd could muster in caucus and Gillard's flat refusal to consider one.
She told Channel Seven there was no need: "I'm very confident in my leadership."
But the next three months will be crucial for her.
Despite renewed avowals of support, a large number of MPs back Rudd or have yet to make up their minds, and they will be carefully watching Gillard's performance and the Government's standing in the polls.
If little has changed by the May budget parliamentary session, support for Gillard could shift further towards Rudd.
The Nielsen results, if confirmed and continued by future polls, should help lift the avalanche of speculation that has overtaken Gillard and buried Government successes.
Nielsen said that after nine months Gillard had finally regained her lead over Opposition leader Tony Abbott as preferred prime minister, albeit by a wafer-thin two-point margin, 48-46 per cent.
Labor's primary vote has risen by four points to 33 per cent since the previous December poll - against a similar slide to 45 per cent for the Coalition - and the Opposition's lead in the two-party preferred vote that decides Australian elections has narrowed to 53-47 per cent. Gillard's support as leader rose five points to 35 per cent, still well behind the 57 per cent who preferred Rudd. But Rudd's vote was four points down, one-quarter of his supporters did not want a challenge, and Labor voters backed Gillard by 50-47 per cent.
Nor was there any public talk of a challenge on Sunday when MPs gathered for a special caucus meeting at The Lodge, the Prime Minister's official Canberra residence.
Gillard was reported to have given a strong address in which she emphasised the need for unity and discipline, and for MPs to focus heavily on economic management, the passage of key reforms, and benefits to come from further measures this year.
Backbenchers who have been pushing Rudd in anonymous media briefings were warned to stop.
Ministers yesterday hit radio stations with the message, supported by MPs angry at what they said were the "exaggerated" claims of Rudd supporters, and furious at a table in News Ltd Sunday newspapers naming supporters of rival groups.
A number said they had not been contacted by reporters.
Trade Minister Craig Emerson told ABC radio yesterday: "Where have they been - in Antarctica for the summer? No one has rung me.
"They make them up as they go along because they want to create the impression that there's a big leadership issue here, whereas in fact the big issue is that Labor is working for and on behalf of the working people of this country."
Yesterday, independent MP Tony Windsor said his guarantee of support for the Government might not survive a change of leader, and warned that a coup would almost certainly force a snap election that Labor would lose. Brown said he expected Gillard to lead the Government into the election.
But Parliament will still be a rough ride for Gillard. Tasmanian independent Andrew Wilkie withdrew his guaranteed support after Labor reneged on a deal on poker machine regulation, leaving the Government with a one-vote majority.
And the decider in any tied vote rests with the new Speaker of the House of Representatives, Peter Slipper, who now sits as an independent after quitting the Liberals last year.
Prime Minister hits out at 'media sexism'
Embattled Prime Minister Julia Gillard believes she is the target of media sexism.
Australia's first female leader told the Seven Network that her male predecessors had not been subjected to the same sort of personal criticisms.
Gillard said she was not surprised that the nation was taking time to adjust.
"I mean I grew up watching the prime ministers of this country and if you'd asked me then 'close your eyes and imagine a prime minister' I would have imagined a bloke in a suit," she said. "I'm the first person to not be a bloke in that suit."
But she said she should be judged by the same standards applied to male prime ministers.
"If we look around at Australia's political history when Bob Hawke was there, when Paul Keating was there or when John Howard was there, I don't actually recall there being constant demands for them to show more personality," Gillard said.
"I don't remember people looking at John Howard and saying, 'Gee, I wish he would be warmer and cuddlier and more humorous'."
Greens leader Bob Brown agreed. "The degree of relentless criticism on this Prime Minister coming from male commentators is sexist and quite ridiculous at times."
