Senior Labor MP Anthony Albanese's public interventions on the federal budget and a controversial "Australians First" advertisement have infuriated colleagues, with some believing he has destabilised Bill Shorten.

Mr Shorten's praetorian guard of supporters are now pushing back, claiming the NSW MP - who fought Mr Shorten for the Labor leadership in 2013 - fears he has missed his chance to lead the ALP.

In the past two weeks, Mr Albanese has publicly criticised the "Australians First" ad as a "shocker", and offered an alternative budget reply speech in which he said Labor should have claimed victory following the "ideological surrender" of the Turnbull government in its 2017 budget.

Fairfax Media has spoken to several Labor MPs who are close to Mr Shorten and who believe Mr Albanese "can see his last chance [to be leader] slipping away".

"This is the last roll of the dice for him ... he is trailing his coat and it is destructive," one said.

Another said he could not understand what Mr Albanese was up to, but "he can't think he's on the cusp of becoming leader when we are on 53-47 in the polls".

MPs close to Mr Albanese, insist he has no designs on the Labor leadership but that as a senior MP and former deputy prime minister he is entitled to speak on issues as he sees fit.

Fairfax Media has contacted the offices of Mr Albanese and Mr Shorten for comment.

Though few in Labor disagreed with Mr Albanese's criticism of the ad, his decision to go public raised eyebrows.

A number of senior MPs, including Chris Bowen and Tony Burke, as well as factional leaders Sam Dastyari and Tim Watts, were furious about the ad, but called Mr Shorten to complain privately, concerned about the need for public unity following the disastrous Rudd-Gillard years.

Fairfax Media has been told by a member of the shadow cabinet that at a meeting on the Monday before the budget - the day that Mr Albanese criticised the ad and Mr Shorten ordered it pulled from the air - the pair had a "robust" exchange.

An MP who was in that meeting said: "Shorten didn't say I am personally sorry [for the ad]; he said someone else stuffed up and agreed it shouldn't have been shown. He then had a crack at Albo about people making public comments.

"Albo then said what he thought, and they moved on."

Mr Albanese had informed the leader's office before a press conference he was scheduled to give that day that, if asked, he would publicly criticise the ad.

While some MPs believe Mr Albanese is correct to have argued the ALP should have "claimed victory" after the 2017 budget, others are annoyed that it has distracted from the opposition's political attack on the Coalition's budget.

On Tuesday, for the second question time in a row, the Turnbull government focused on revelations published by Fairfax Media on Monday that Labor's shadow cabinet was split over whether to back the 0.5 per cent rise in the Medicare levy for all taxpayers, or just those earning more than $87,000.

Prime Minister Malcolm Turnbull mocked Mr Shorten for "defying the wishes of the majority of his own shadow cabinet", who had argued Labor should back the rise for everyone to help fund the National Disability Insurance Scheme.

Deputy Prime Minster Barnaby Joyce, backed by catcalls from government benches, told Parliament: "He [Mr Albanese] has never asked a question, he is not allowed. He sits there, he is almost mute. He is in the race, he is in the race for this fellow's [Mr Shorten's] job; that is why he can't ask a question."

On Monday, Labor deputy leader Tanya Plibersek defended the decision to impose the Medicare levy rise only on people earning more than $87,000, and disputed that a majority of the shadow cabinet had backed a rise for people on all incomes.

"We made a decision that protecting 10 million taxpayers, 80 per cent of taxpayers from a tax increase, at a time when wages growth is at historic lows, was the right thing to do," she told the ABC.

"The fact that a conversation - a friendly conversation between colleagues with different views - makes it to the paper shows how little we talk about what happens in shadow cabinet, and that's a good thing."

However, former Labor trade minister Craig Emerson argued in the Australian Financial Review the ALP should have backed the levy rise for all income levels.

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