One of the former PM's supporters has told the ABC that Mr Rudd is now about seven votes short in the event of a leadership challenge, although Ms Gillard's backers dispute this.
Speaking to reporters outside a church service this morning to mark the start of the parliamentary year, Mr Rudd said Labor's "core challenge" was to do everything possible to make sure Opposition Leader Tony Abbott does not win the election.
"That's my mission in life and that's what I'll be doing this year," he said.
Asked if his supporters were counting the numbers for a leadership challenge, Mr Rudd said: "Oh give us a break, you know, give us a break".
"I said 12 months ago that I supported the Prime Minister... (and) that remains my position and everyone should take a very long cold shower."
Mr Rudd launched an unsuccessful challenge against Ms Gillard's leadership in February last year. She won the vote 71 to 31.
But there has been internal criticism of the Prime Minister's performance over recent weeks following her decision to announce the election date nearly eight months ahead of polling day, her dumping of incumbent Northern Territory Senator Trish Crossin, and the resignations of two senior ministers.
Ms Gillard yesterday told her colleagues that she knew some of them were briefing the media against her, and urged the party to unite.
This week's Newspoll showed a dramatic slump in support for the Government, prompting one of Mr Rudd's most vocal critics to suggest that it would be a "fantastic boost" for Labor's fortunes if the former prime minister was to campaign beyond his Brisbane electorate.
"I think he is an asset and we should use him. But it has to be a disciplined asset," frontbencher Simon Crean said.
Fellow Labor frontbencher Anthony Albanese agreed that Mr Rudd was an "asset" that should be used wherever possible.
"He's a very popular figure, there's no doubt about that," he said.
Speaking to reporters again on the way out of church, Mr Rudd said he would be campaigning in Labor seats across the country, adding that the commitments had been locked in before the "hoopla" of the last couple of days.
Mr Rudd last week returned to Channel Seven's Sunrise, the television show that helped propel him into the Labor leadership and ultimately the Lodge.
He has also sent a letter to "young people" in his Brisbane electorate of Griffith, inviting them to participate in "Barefoot Bowls with KRudd", with the Twitter hashtags "#ruddyrollin" and "#winning".
The letter, which does not include Labor Party branding, begins with, "Politics can become a little boring. But it doesn't have to be".
Labor Minister Greg Combet says he does not want to get distracted by talk of leadership, adding that Ms Gillard has "strong support" within the Caucus.
"I don't pay much attention to the leadership speculation. We've got a team, we're firmly behind it. We're going to argue our case for the rest of the year," Mr Combet told ABC News 24.
"What matters to people is the dental reforms we're making, the health reforms, the improvements in education, the development of a National Disability Insurance Scheme."
Deputy Liberal Leader Julie Bishop has told colleagues that she believes Mr Rudd has "one more tilt" at the leadership left in him, but has also raised the prospect of Senator Bob Carr positioning himself for a promotion.
Addressing today's joint Coalition party room meeting, Ms Bishop described the Prime Minister as the Coalition's greatest asset, and reminded them of the long-standing political advice never to interrupt your enemies while they are fighting against themselves.