How could Julia Gillard's leadership implode so quickly and spectacularly just a few months after her decisive win over Kevin Rudd?

That is the dreary question facing Labor MPs this weekend. There is no clear answer and no obvious way to avoid electoral disaster.

In the short term they are extremely worried that ongoing debate about the PM's political judgment will overshadow the merits of the budget. And so they should be, given the disillusionment abroad in the community.

If so, that could be the end for Gillard. And if that happens, she can't blame Kevin Rudd.

Earlier in the year, the media was blamed in part for creating speculation about Rudd's ambitions. Now, ministers are again suggesting the new bubble is a media fabrication.

''I don't believe the leadership is an issue for us,'' government Senate leader Chris Evans says.

But the polls expose the grim reality of very low support for Labor.

Why else would one of the PM's chief supporters, Greg Combet, tell the team to ''hold their nerve''?

The quietly spoken minister is charged with selling the merits of the carbon tax against the barrage of Tony Abbott's shrill negativity. It's not an even match.

But Combet says he recently managed to calm fears about the tax at a community meeting when he spent a lot of time patiently answering questions. ''There's no doubt that the politics with the carbon price are difficult,'' he says.

That is especially the case when a high profile Labor figure such as Kristina Keneally urges Gillard to dump or wind back the carbon tax.

Keneally publicly supported the tax in the losing NSW election campaign but are we now hearing her truthful opinion? ''Whether it's good policy or not is now irrelevant - it is completely bad politics,'' she says.

With the broken promise on the carbon tax undermining trust in Gillard, Keneally urges the PM to act, and apologise. ''In doing so, she would tell the people of Australia, 'I am sorry and I am listening to you'.''

How many are still listening now?

If the Prime Minister could meet every Australian - so the adage goes - she might win many over. But she would have no chance with those who are confronting Labor MPs at shopping centres and unleashing unprintable language about the Prime Minister.

This depth of hatred is now evident in some regions, particularly Queensland, according to backbenchers.

However, a Victorian MP also says, ''I can't go anywhere now and set up a mobile office without people sounding off about her in very crude language.''

Gillard's broken promise just won't go away, and is kept alive by Abbott's ceaseless campaign. Her future is being likened to Anna Bligh, dumped by voters in brutal fashion in payback for backflips on privatisation and petrol subsidies.

So where to from here? Yet another backflip on the carbon tax? A partial backdown?

The government could lower the $23-per-tonne starting price or announce a move to an emissions trading scheme earlier than planned in mid-2015, which would also lower the price. It could also offer a one-off utility payment to soften the impact of the carbon tax or boost the household assistance.

A worried Labor MP says people have seen through the bright wrapping of the assistance package.

''You only give compensation when something hurts, and all this talk about generous assistance only draws attention to the reason it is needed,'' the backbencher says.

If the budget does not give Gillard a boost, the despair among Labor MPs will deepen and the PM's support will erode further. So time is running out for a compromise or sweetener for the carbon tax if, that is, Gillard decides she wants to offer one.

When asked directly on Thursday about changes to the compensation, she sidestepped the issue, preferring to point, again, to the compensation payments, some of which begin before the July 1 start date of the carbon tax. ''People will see the cold hard cash very, very soon.''

Alternatively the PM could decide to lift her game on selling the environmental benefits, given that many Australians want something done about climate change. But Abbott long ago outflanked her by framing the debate on the carbon tax as an economic issue.

When Gillard finally made up her mind on Peter Slipper and Craig Thomson, it was a good decision. But it was so delayed by procrastination or bad judgment - or both - that it was simply too little, too late.

The nation had moved on, running the ruler of ordinary decency over the case of both men. Gillard was way behind, sticking clumsily to the presumption of innocence without seeing the wider picture.

She did show good judgement earlier in the year when she forced Rudd to bring on his run for the leadership before he was ready. She combined that with very strong attacks on his character from her senior ministers.

In the lead-up to that leadership ballot, Rudd's support in caucus flat-lined, not rising above the proportion who had been loyal to him ever since he was dumped two years ago.

As a result of the limited caucus support and the explanation finally given to Australians about why he was dumped, Rudd's political career is over. Or is it?

Political orthodoxy would say yes. Why then is speculation in the caucus and the media swirling around a return to Rudd - or Simon Crean? How mad is this?

At least seven senior ministers have sworn to resign if Rudd returned as leader. And the Liberal Party would have ready-made ads, using the very public statements by ministers who savagely accused Rudd of sabotaging the election campaign with cabinet leaks.

This week's renewed and feverish leadership speculation was sparked by Gillard's stumble when she said a line had been crossed in the scandal surrounding Thomson and the Health Services Union - and was then unable or unwilling to explain what she meant.

''Coming back to Australia, being right here now, I have felt very sharply the judgments and concerns of the Australian people,'' she said.

Doesn't that mean she misread the situation? She ducked and weaved. Why not say she got it wrong, if that was the case, and move on?

This lack of clarity - or worse, the appearance of deliberate obfuscation - sparked the week-long wobbles. As one Labor MP put it, ''The leader was given clear air and she has dropped the ball, again.''

Is Gillard listening to bad advice, or refusing to take good hints? Labor was hoping that this week would be a positive springboard to the budget, which in turn would be the kick-off for a political revival.

Now a sceptical public will be watching carefully for smoke and mirrors as Wayne Swan switches the bottom line from a $40 billion deficit to a $1 billion surplus in just one year.

The rampaging Opposition is already practising its preferred phrase, claiming the government is set to ''cook the books''.

Abbott will try very hard to undermine the budget, because he knows how very important it is for the Gillard administration.

The budget must become a turning point for Gillard by demonstrating, once and for all, that Labor can be trusted with the economy.

To earn credibility, it must give a big dose of ''tough love'' to demonstrate Labor's economic credentials, but this implies a big hit against Canberra's public servants if, as Gillard is warning, there will be ''deeply unpopular'' cuts to programs.

Ross Peake is Political Editor.

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