Tim Fischer and John Anderson, who served as deputy prime ministers under John Howard, told Fairfax Media the party had to stop disputes over the leadership and help fix a "trust deficit" with voters that was fracturing Australian politics.

"There is a federal election coming and the last thing the Australian people want is any confirmation that white-anting has taken a permanent place in the Australian political landscape," Mr Anderson said.

The Coalition is bracing for its second leadership challenge in less than two months as Nationals MPs count the numbers to topple Deputy Prime Minister Michael McCormack as soon as Tuesday.

The unrest has infuriated the Liberal Party, which is fighting to retain its one-seat majority at Saturday's crucial Wentworth byelection.

Mr McCormack insisted on Thursday his colleagues had not complained to him about his performance and his core supporters warned against a spill, saying it would be an electoral disaster to restore Mr Joyce just seven months after he resigned in disgrace over an affair with a staffer and a separate allegation of sexual harassment.

Mr Anderson likened the party to a ship in trouble ahead of the next election after the sudden resignation of Mr Joyce in February.

"It’s really important that we recognise that it’s very hard to pick up the baton when the captain on the bridge finds that he can’t navigate the ship anymore and you unexpectedly find, having not been prepared because there was no reason to prepare for it, that you’re in charge of the ship yourself," he said.

"He deserves the support of his fellow officers and they need to pull together now to save the ship, not argue over who is going to be the captain."

Mr Joyce has denied canvassing votes but his Queensland-based backers have been counting the numbers. MPs agitating for change have discussed forming a delegation to ask Mr McCormack to resign, fearing a wipeout in Queensland at next year's federal election.

Some of Mr McCormack's own supporters believe the Deputy Prime Minister could command just eight votes out of the 22-member party room if a spill is called when Parliament resumes next week. Another option being canvassed is a move in late November or early December.

"The fact is I have the majority support in the National Party," Mr McCormack said.

"Not one National Party member has come to me and said they're dissatisfied with anything."

Mr Fischer told Fairfax Media that Mr McCormack deserved more time to stamp his authority on the party and build his profile.

“Michael McCormack has covered more ground than I ever did in the seven months he has been leader and Deputy Prime Minister," Mr Fischer said.

"I think everyone should go back to their electorates, lie down and have a Bex."

A switch back to Mr Joyce would guarantee his return to cabinet and trigger a wider frontbench reshuffle just two months after Prime Minister Scott Morrison's new-look ministry was sworn in at Government House in Canberra.

Nationals senator John Williams said he had not been approached by any camp but acknowledged "someone" is leaking against the Nationals leader and likened the situation to pouring petrol on a fire.

"It grows and grows," he said.

The senator said he was "surprised" Nationals MP Michelle Landry had publicly predicted Mr Joyce would eventually return to the leadership.

"I think Michael needs time and he will get time, I have no doubt about that," Senator Williams said.

Agriculture Minister David Littleproud – who is widely viewed inside the government as a future Nationals leader – has ruled himself out of running in any spill.

Mr Fischer said a Nationals leader needed to be a unifying figure in all parts of the country, not just Queensland.

“I am backing Michael. I think he is off to a flying start. He needs to continue to step up in that role. And in so many ways it's important to bridge the very real Brisbane line," Mr Fischer said.

“There is a gap in what flies north of the Brisbane line versus what happens south of the Brisbane line.

“Until you learn how to come up with the right set of words that cuts through both sides of the Brisbane line, you will be done over, on nothing more so than the issue of multiculturalism."

Nationals deputy leader Bridget McKenzie said Nationals MPs had a tradition of waiting patiently for leaders to retire before they rose to the leadership.

Mr Anderson said Mr Joyce needed to recognise "what is required" if the Coalition was to have "any chance" at the next election.

"The enemy at the moment is an alternate government that will take this country back to the utterly failed policies of the 1950s and the 1960s," Mr Anderson said.

The former leader also pointed to wider fault lines in Australian politics.

“The trust deficit in the system of politics, our major institutions, the banks, the churches, the media and even academia today is very serious," he said.

“Western democracies have always depended on a high level of trust. There has to be confidence that people will do what they ought to do, not be coerced into what they should do.

“So we as Australians need to recognise that this is very serious and that, over the last five decades in particular, we have atomised and fractured our society.

“To some extent this is showing up in our politics. It’s not just being driven by politics and the 24-hour news cycle, it’s being driven in no small way by the atomisation of our culture – in common with all other Western countries.”

Sydney Morning Herald