Freshly re-elected deputy leader Julie Bishop insists Malcolm Turnbull will make it to the end of the week. But the flurry of resignations from his cabinet late on Tuesday night may suggest otherwise.

“Frankenstein’s monster of a government” was how one Labor frontbencher, Tanya Plibersek, derided the chaos in an explosive question time. It has the face of Mr Turnbull, the policies of Tony Abbott, and the “cold, shrivelled soul” of Peter Dutton, she said.

Some of those stitched-together body parts fell away on Tuesday night, with at least five members of the ministry tendering their resignations: James McGrath, Michael Sukkar, Concetta Fierravanti-Wells, Angus Taylor and Zed Seselja. All were among the 35 who backed Mr Dutton in the leadership ballot earlier that day.

Mr Turnbull refused most of the offers, hoping instead to heal the wounds, but  did accept International Development Minister Ms Fierravanti-Wells’ resignation after she wrote a scathing letter.

Trade Minister Steve Ciobo, Human Services Minister Michael Keenan and Health Minister Greg Hunt also reportedly offered to resign after it was reported they had also voted for Mr Dutton, with Mr Ciobo and Mr Keenan releasing statements offering support to the Prime Minister.

Mr Turnbull reportedly asked the ministers to stay on.

The ABC on Wednesday morning reported Citizenship Minister Alan Tudge also offered to resign, but agreed to remain in the role and continue serving under Mr Turnbull.

The deputy leader, Julie Bishop, stood firm even as news of the resignations flashed across the screen beneath her on ABC television.

“These are people who, for their own reasons, have decided to offer their resignation,” she said.

“But I know that the Prime Minister is working very hard to heal the divisions and to bring the party together.”

Julie Bishop denied to the ABC that she was canvassing an attempt at leadership. Photo: ABC

It remains to be seen whether Mr Turnbull’s attempt at healing by refusing to accept the resignations will placate the disaffected.

The erosion of support will have hurt, especially as it included Mr McGrath, who was reportedly instrumental in helping Mr Turnbull seize power and was assistant minister to the PM himself.

But Ms Bishop stuck to her lines, saying she believed Mr Turnbull’s prospects would now improve, and that he would still be leader at the end of the week.

And would she, as second most popular leadership option after Mr Turnbull, according to recent polls, consider a challenge?

“I’m not canvassing that option,” Ms Bishop replied.

Ms Bishop may prove one of the main impediments to Mr Dutton’s rise.

There are reports she has threatened to quit the frontbench, perhaps even the Parliament, rather than serve under a Dutton prime ministership.

Add to this the claims that four Nationals MPs are reportedly willing to sit on the crossbench, because they do not believe Mr Dutton is electable in the southern states.

There are also questions around whether Cathy McGowan and Rebekha Sharkie would continue to give confidence and supply to a Dutton-led government.

Mr Turnbull has threatened several times, openly or by implication, to quit and trigger a damaging by-election whenever leadership questions have arisen in the past.

This may pose a tricky dilemma for Mr Dutton, who for now is playing it safe. In an exclusive interview with Sky News he did not rule out a future challenge, nor did he give away his policy agenda – apart from hints at hot button issues such as immigration. He was also tight-lipped on whether he would welcome Tony Abbott into his ministry.

What he did try to do – clumsily, according to many commentators – was soften his hard man image.

Almost Mr Dutton’s first words when fronting the media on Tuesday afternoon was to say he was glad to finally be able to smile more, now that he was free of responsibility for border security. He repeated the line to Sky News.

“I can smile … I want to smile again … I want Australia to have an opportunity to see the real me.”

When pushed on what this ‘real’ and more likeable Mr Dutton looked like, he said he liked a drink, had a “self-deprecating” sense of humour, and liked to watch a kid’s footy game on the weekend.

But some old tweets soon came back to haunt him.

Some friendly advice Julia – beware a D/PM selling his "softer" side at a time your party is looking for l'ship

— Peter Dutton (@PeterDutton_MP) April 20, 2011

Latika must have a date after qn time? Wearing big new dangly earings and a big purple flower.

— Peter Dutton (@PeterDutton_MP) February 9, 2010

You dirty lefties are too easy. Enjoy your weekend.

— Peter Dutton (@PeterDutton_MP) December 9, 2011

So far, Mr Turnbull has won little praise for his backflip on energy policy. And there is no news yet on the fate of the big-business tax cuts, which he has also watered down, by reportedly offering to carve out the unpopular big banks.

Senator Mathias Cormann, a staunch Turnbull supporter who is widely considered a bellwether for whether Mr Turnbull keeps The Lodge, has admitted the tax cuts are “not politically popular”.

But, speaking in the upper house earlier in the day, he urged his colleagues to not merely “follow the lead of public opinion at one particular point in time”.

Labor seized on the confusion and chaos by interrupting question time to move a motion of no confidence in the Prime Minister. In a historic move, Mr Turnbull accepted the challenge, allowing the motion to be debated, perhaps in an attempt to appear strong.

It may not have helped, as his frontbenchers appeared keener to slam Bill Shorten than defend him.

It also gifted Labor national television coverage of five of its best-known attackers – Mr Shorten, Tanya Plibersek, Tony Burke, Chris Bowen and Anthony Albanese.

“Australia has a Prime Minister in name only. Without power, without policies,” Mr Shorten said.

Peter Dutton is a “really scary wooden puppet” with Tony Abbott’s hand up his “… back”, said Ms Plibersek. That image, and the deliberate pause, must have riled Mr Dutton, as he later told Sky News: “I am not a puppet.”

Mr Burke had the Labor benches crying out “doomed” in unison as he recounted each policy backflip.

And Mr Albanese branded them the “NO-alition” and the “opposition in exile”.

So will Malcolm Turnbull survive the week? The more common question, asked by many commentators, is whether he can last to Thursday, when Parliament rises for the week.