Australian politics has been markedly wild the last few weeks, culminating in Prime Minister Tony Abbott's admission that he broke key election promises. Given how long it's taken for us to get to this point - where to go from here?

Let us not beat around the bush - Abbott is now, well and truly, Australia's George W Bush. But before we delve into the implications of this, we should note that this is hardly a newly apt title.

For one thing, this is not the first promise which Abbott has broken. In a now infamous interview on public television the night before his election, Abbott made a series of promises to voters: "No cuts to education, no cuts to health, no change to pensions, no change to the [goods and services tax] and no cuts to [the public broadcasters] ABC and SBS."

In office, Abbott's government cut $80bn earmarked for schools and hospitals, pursued policies which would increase the costs of tertiary education, sought to change pensions, and is now cutting funding to the public broadcasters.

"Politicians make promises," I hear you say, "and they break them. Nothing new".

Not inconsequential

Yes, although these aren't inconsequential or small promises to break. Perhaps more importantly, though (at least in a political sense), is that Abbott ran his 2013 election campaign on trust.

Abbott's opponent in 2013, then Prime Minister Kevin Rudd (once ousted by his deputy, Julia Gillard) was looked at with suspicion by voters due to the internal turmoil within his party. Further to the theme of trust, when in opposition, Abbott was unwavering in his attack on Gillard's broken promise to not introduce a carbon tax scheme, which she later did.

So Abbott might have dug his own grave, it seems; his popularity has plummeted; several of his proposed cuts have failed or proven intensely difficult to pass through parliament; and even light-hearted breakfast television interviews with jolly holiday decorations in the background don't turn out well. Perhaps this is the story of how the Grinch stole Christmas? If so, what will be the carol that brings the Grinch back with Australians' pensions, education, health, and the rest?

A key feature of Australia's parliamentary system is that it allows for the forced removal of prime ministers - along with anyone else holding public office. This is in stark contrast to the presidential system in the United States, for instance, where no matter how unpopular a current president, only the likes of impeachment have such potential. And while US conservatives might regularly threaten such proceedings against President Barack Obama (should he enact particular executive orders to advance his policies), only three sitting presidents have had articles of impeachment brought before them. Such proceedings are also not designed for removing unpopular presidents, only those who have allegedly committed a crime while in office.

Meanwhile, in Australia, there are two possible ways for removing unpopular leaders, and neither method require them to have allegedly committed an offence.

Potential for change

First, the more likely: As was the case for the leadership spills or "coups" which befell Kevin Rudd and Julia Gillard at different times, and caused them to be removed as prime ministers of Australia, it is possible (and probably politically preferable) for their caucus to hold a formal ballot. A simple majority in the caucus decides the matter, and is often prompted by unfavourable polling or dissent among the caucus ranks.

To stay in power, Abbott's party may need to change leader. Whether they do or not, though, the Australian public has already made it clear that the conservative government's significant, proposed cuts were a step too far.

In this case, the potential for change relies upon Abbott's party. While such a change may be beneficial for the party in the short-term, insofar as ridding the negative image of Abbott, it might not be an opportune moment for such a change. Part of what saved Gillard's party from defeat in the 2010 election was her replacing Rudd (who was unpopular at the time) and immediately calling a fresh election, capitalising on the political honeymoon period which followed the leadership swap.

For this reason, Abbott's party may remain strategically patient, waiting to pounce at a more appropriate time. Nevertheless, even if they did decide to change leaders, they don't have many good options - two of the main contenders, Treasurer Joe Hockey and Communications Minister Malcolm Turnbull, have been implicated with the harsh budget and Abbott's broken promises.

The second and more controversial way to oust a sitting prime minister is for the governor-general, the Queen's representative in Australia, to dismiss the prime minister, as happened to Gough Whitlam in 1975 - much to his displeasure. Given how bitterly contentious this method became after it was first used against Whitlam, and how many - including, allegedly, the Queen herself - were concerned about its use, it is very unlikely that it would be used again. However, according to Australia's constitution, it remains possible.

International ramifications

To stay in power, Abbott's party may need to change leader. Whether they do or not, though, the Australian public has already made it clear that the conservative government's significant, proposed cuts were a step too far. Accordingly, if the government wishes to remain the government, they will need to move their policies towards the centre of the political spectrum to regain public support.

If, for example, Abbott is replaced by someone like Turnbull, the world could expect a few key changes in how Australia engages in international politics. For one thing, Australia would no longer be a non-contributor to climate change reduction efforts, such as those recently announced by the US and China. Turnbull is a vocal supporter of action on climate change, whereas Abbott is a climate change denier and once described the related science as "crap".

Another possibility is that other prominent moderates could influence change to Australia's asylum seeker policies, which the United Nations have repeatedly condemned for their inhumanity.

When and if these changes eventuate is open to speculation, but what most certainly is not is that Abbott's government has had a bad few weeks and is likely to have a few more. Stay tuned for the carols.

Tom Burns is an Australian writer who studies bioethics and neuroscience. His work has been featured online and in print in Australia and abroad.