There's been an enormous amount of distraction about this week.

Kevin Rudd itching to capture Tripoli. Julia Gillard delivering a beautiful speech to a room full of people who can't vote for her. Tony Abbott taking this opportunity to visit a steel mill in the PM's own electorate with his terrifying artist's impression of what her new carbon tax might look like.

Tony Windsor, complaining about the Prime Minister's decision to announce the prospect of a carbon tax without supplying any detail (provoking, in uncharitable minds, the question about why Mr Windsor himself chose to stand beamingly next to her while she did so).

As regular readers will know, your correspondent is going cold turkey on Newspoll, AC Nielsen and their ilk this year. But even the virtuous abstainer cannot ignore the blow to Labor's solar plexus landed on Tuesday (a day I spent chain-smoking, and calling my Pollaholics Anonymous sponsor every seven minutes).

One columnist even started the old "No-one is counting numbers for a challenge, but people are talking about alternatives to Gillard" drum-beat.

Let's look at the basics here.

Labor's problem is one of trust and consistency.

Political advocacy is about believing something, and setting out to bring a majority around to your point of view. In the best political advocates, principle and determination work together to the extent that even voters who fundamentally disagree with their position on a particular policy stance will grudgingly support them anyway.

Federal Labor is a long way from that right now, thanks to the messages it has sent out to the electorate on a number of issues.

Climate change, for example, where its message has been: "This is the most important moral challenge of our... oh, never mind. Wanna be in a focus group? Course there won't be a tax. Wait! I know! How about a tax?"

Or border protection: "Tough! Humane! Tough! Humane! I'm on a boat! No, you're on a boat! Look, there's East Timor! And there will be no new detention centres. Except for that one we're building right there."

Or health: "We're taking this thing over. Or maybe not. I'm wearing a mob-cap. Wait! We fixed it! Oh, bugger. Maybe we didn't. How about this?"

All the questions that are zinging around about the carbon pricing scheme right now are predictable, and fair enough.

Such questions will always attend a policy that is under development in the public eye. But the fundamental question that lies beneath all of them is far deeper, and more profound, and far more risky for Julia Gillard than what the price per tonne will be or what the carbon tax will mean for a birthday cake.

And that question is: Can this prime minister possibly build, in the hearts of her admirers and detractors alike, the unshakeable belief that she means what she says?

What is the answer? I don't know. I think, given the circumstances, that it's a pretty long shot.

But I suspect that anyone who is idly contemplating leadership change probably hasn't quite twigged to what the core problem is.

Can you imagine what would happen if federal Labor swapped leaders again? The analogy with rotten NSW Labor would be complete. You might as well just go ahead and get Craig Emerson to hop up on his desk and dance in his undies.

The image of the Labor Government - a wobbly invertebrate, yanked hither and thither by hidden factional puppeteers - would be confirmed.

And the sweating independents, for whom daily life is made more difficult every time their coalition partner buggers something up - would presumably take the opportunity to decamp to Tony Abbott, or force an election.

The whole idea is so suicidal and daft, in fact, that you probably can't rule it out entirely.

But make no mistake about what the issue is here.

Annabel Crabb is ABC Online's chief political writer.