Tony Abbott refuses to concede that he broke any promises with his first budget. Will this approach prove more successful than Julia Gillard's ill-fated acquiescence on the carbon tax? Annabel Crabb writes.

As it's becoming increasingly unoriginal to point out, all governments break their promises to some extent. What makes them different is how they handle it, and the events of the last week suggest that Australian politics is currently experiencing a genuine Sliding Doors moment.

When you are accused of breaking a promise, there are two options. The first is to cop it sweet, in an attempt to kill the argument so that everyone will move on. The second is to have the argument, in the hope that everyone at some point will get sick of arguing.

Each technique has its advantages and disadvantages. Julia Gillard chose the first, and Tony Abbott seems at this stage to have plumped for the second.

In 2010, when Ms Gillard enlarged upon her campaign promise not to impose a carbon tax by getting together with the Greens and agreeing to impose a carbon tax, she did have the option of arguing the toss.

A three-year fixed price on carbon emissions, yielding thereafter to a floating price as part of an emissions trading scheme, could, at a pinch, have been defended as "not a tax". But the then PM ceded the argument. Why? Perhaps she didn't want to exacerbate a broken promise with sneakiness. Perhaps she envisioned months of semantic debates conducted up hill and down dale at press conferences, doorstops and radio interviews and decided that no fate could possibly be grimmer. Perhaps it was just a colossal piece of misjudgement; certainly, there are former colleagues of hers who hold that view.

Would life have been easier for her, would "Carbon Tax" be a phrase less fierily branded upon the Australian political consciousness, had she stood her definitional ground?

It looks like we're about to find out.

Tony Abbott and Joe Hockey do not concede that their government has broken any promises. They have opted to bat on, invoking - depending on which day it is, and with varying degrees of success - one or all of the following defences:

The impost on high income earners is not a new tax, because it's actually a temporary levy that runs only for three years. (This defence is so similar to the one Ms Gillard chose not to use that it's freaky.)

The impost on high income earners is not a new tax, because it's actually a temporary levy that runs only for three years. (This defence is so similar to the one Ms Gillard chose not to use that it's freaky.) The petrol excise hike is not a new tax. It's an increase to an existing one, and nobody promised taxes wouldn't be changed.

The petrol excise hike is not a new tax. It's an increase to an existing one, and nobody promised taxes wouldn't be changed. The pension changes aren't scheduled to happen until after the next election, and the other cuts affecting pensioners, like reduced concessions, aren't actually changes to the pension itself, so that's not a breach of the promise not to touch the pension.

The pension changes aren't scheduled to happen until after the next election, and the other cuts affecting pensioners, like reduced concessions, aren't actually changes to the pension itself, so that's not a breach of the promise not to touch the pension. The spending cut from the Commonwealth health budget is going to be directed to medical research, so that doesn't constitute, definitionally, a "cut to health".

The spending cut from the Commonwealth health budget is going to be directed to medical research, so that doesn't constitute, definitionally, a "cut to health". Because the Coalition will abolish the mining and carbon taxes, the overall tax burden will be lower, thus fulfilling in a more global sense the promise not to raise taxes.

Because the Coalition will abolish the mining and carbon taxes, the overall tax burden will be lower, thus fulfilling in a more global sense the promise not to raise taxes. The Medicare co-payment might be a tax, but on the other hand it might be a rabbit.

The up-hill-and-down-dale element to the argument is unfurling exactly as you might have expected. Do Tony Abbott and Joe Hockey have the requisite stamina?

Mr Abbott, who runs up hill and down dale as a personal hobby, seems to be up for it. Mr Hockey, who is being asked to carry the political opprobrium for breaking undertakings which overwhelmingly were made by his leader and not by him (and often, indeed, were made by his leader to Mr Hockey's significant personal discomfort), might find it rather heavier going.

Much has been made of the polls this week, in which Mr Abbott's popularity declined from where it had been hovering - around the "stubbed toe" mark - right down to "fart in a crowded elevator" depths. Predictions that this would prove the beginning of the end were immediately available.

I don't know about that. Mr Abbott has never been a popular figure. He was unpopular before the election, and the budget has made him even more unpopular. Obviously, in a democracy, unpopularity is a problem. But popularity has its own problems, too; leaders who are massively popular can often become so obsessed with remaining so that they are incapable of doing anything, lest people change their minds.

This was a persistent problem for Kevin Rudd; one might respectfully conclude it's not going to trouble Mr Abbott too much.

Annabel Crabb is the ABC's chief online political writer. View her full profile here.