Julia Gillard is expected to announce a caucus vote on the leadership issue today, which will be held when federal parliament resumes on Monday.
Mr Rudd quit as foreign minister yesterday, halfway through a visit to Washington, amid speculation the prime minister was preparing to sack him for disloyalty.
It is believed Ms Gillard was planning to sack Mr Rudd before parliament resumed on Monday as she was under pressure from the two key independents, Tony Windsor and Rob Oakeshott.
Both said they would not be in favour of a leadership change.
Mr Windsor reaffirmed yesterday he may walk away from Labor, possibly forcing an election.
Mr Rudd may potentially try and win the support of Queensland independent Bob Katter to ensure some support if the other two walk.
Mr Katter said yesterday he was not one of the crossbenchers "who delivered the present government" and is not interested in Labor's internal workings.
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Mr Rudd, who will return to his home city of Brisbane tomorrow, said he would consult his family and colleagues before making a final decision on his future.
But the odds are that he will challenge, given his remarks on the difficulties facing the minority government, which is languishing in the opinion polls.
"Ladies and gentlemen, there is one over-riding question for my caucus colleagues, and that is, who is best placed to defeat Tony Abbott at the next election," he told reporters called to a surprise press conference in Washington after 1am (US time) on Wednesday.
On current numbers, Mr Rudd, who did not discuss his decision to resign with Ms Gillard, is likely to lose the ballot and be banished to the backbench — where he could campaign unfettered.
His other option is to vacate his seat, which would bring Labor an unwelcome by-election in his Queensland seat of Griffith.
Ms Gillard, who took three hours to respond to Mr Rudd's resignation, said she was disappointed Mr Rudd had not raised his concerns with her.
She also praised Mr Rudd's time as foreign minister, saying he was "strong and effective".
But there were no kind words from Deputy Prime Minister and Treasurer Wayne Swan who said Mr Rudd put his self-interest ahead of the party and the broader labour movement and was undermining the government at every turn.
"The party has given Kevin Rudd all the opportunities in the world and he wasted them with his dysfunctional decision making and his deeply demeaning attitude towards other people including our caucus colleagues," he said in a scathing statement on his fellow Queenslander.
"Colleagues are sick of Kevin Rudd driving the vote down by sabotaging policy announcements and undermining our substantial economic successes."
Mr Crean earlier this week mounted the second of two recent attacks on Mr Rudd, amid speculation he was heading toward a challenge to Ms Gillard.
He has said Mr Rudd is not a team player, is a prima donna and will never be prime minister again.
Victorian MP Steve Gibbons on Sunday publicly branded Mr Rudd a "psychopath" after a video was released anonymously on YouTube showing the then-prime minister banging a table and swearing.
As of Wednesday evening it was understood Mr Rudd could bank on the support of between 30 and 35 caucus members in a ballot, while Ms Gillard had about two-thirds on her side.
A member of the Rudd camp told AAP it was warned about Mr Rudd's intention to resign, did not know what he would do next and agreed he was a long way from winning a vote.
Mr Rudd also took aim at Labor's factions and those who helped Ms Gillard into power in June 2010.
"I promise you this - there is no way, no way, that I will ever be part of a stealth attack on a sitting prime minister elected by the people," he said.
"We all know that what happened then was wrong, and it must never happen again."
However, one frontbencher told AAP said it was "funny" that Mr Rudd was talking about faceless men when he had his own, who had been talking him up over the past two months.
"If there is a ballot he will lose," this person said.
Labor senator Doug Cameron said the same "faceless men" in Labor who helped dump Mr Rudd had now forced Mr Rudd's resignation and this was "unacceptable".
"This must just stop within this party," Senator Cameron told ABC television.
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