Tony Abbott appears set to hold onto the Liberal leadership, despite some backbenchers agitating for a vote next week.
There's a feeling among MPs the prime minister is on borrowed time and has up to nine months to turn the government's fortunes around.
West Australian and Queensland MPs Dennis Jensen, Warren Entsch and Mal Brough want the leadership question resolved quickly - possibly as early as next Tuesday, when the party room meets for the first time this year.
And one of Mr Abbott's previously strong backers, Arthur Sinodinos, says the prime minister no longer has his unconditional support.
Some sources within the Liberals are quoting a figure of at least 30 supporters for a spill, not near the majority needed to pass the motion, while others say the numbers are more like 10-15.
Asked whether he would step aside to test his support on Tuesday, Mr Abbott said no-one wanted to return to the leadership chaos of the Labor years.
"I am determined to deliver steady, stable, solid, dependable government," he said.
Senator Sinodinos, a former chief adviser to prime minister John Howard and previously Mr Abbott's assistant treasurer, said his support was based on the prime minister's Abbott's capacity to make the right calls.
"But that support ongoing is not unconditional," he said.
"It's based on being able to grapple with the issues we face at the moment which appear to have impacted on our standing in the polls."
He said the leadership speculation was "not just media hype".
But government Senate leader Eric Abetz dismissed it as "a lot of hyperventilation over nothing".
Fireworks are expected at the party room meeting on Tuesday, but few in the government believe there will be a change of leader.
Polls show strong public support for former leader Malcolm Turnbull, with Foreign Minister Julie Bishop a close second.
A spokesman for Mr Turnbull denied media reports the communications minister had been phoning MPs to canvass their support, while Education Minister Christopher Pyne said Mr Turnbull had personally offered him that assurance.
And Ms Bishop said she wasn't campaigning either.
"I am not contacting the backbench and I am not seeking their support," she said outside an event at the Australian National University.
"I am overjoyed being the foreign minister. I am now living my dream."
Earlier on Wednesday, she declined to rule out standing should the leadership be declared vacant.
"I should not be called upon to rule out what I'm clearly not doing," Ms Bishop told the Australian Financial Review.
Former Victorian Liberal premier Jeff Kennett described Mr Abbott's leadership as terminal.
Treasurer Joe Hockey said any MPs who wanted leadership change should publicly declare their hand.
"If there are dozens, come out dozens," he told reporters before heading into the second day of a cabinet strategy meeting.
One Liberal MP told AAP there was a strong view that Mr Abbott should be given a chance to deliver on his promise to consult more and ditch unpopular policies such as the Medicare GP visit co-payment.
"If there was a vote, Abbott would wipe the floor with everyone else," the MP said.
However, MPs want to see a significant improvement in the government's standing by October.
A longstanding critic of the government's direction, Queensland senator Ian Macdonald says there should be no spill.
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