It’s time for Tony – and Julie and Malcolm – to stop digging. The government is in a couple of truly untenable positions. It keeps digging itself in further.

Take climate change. Tony Abbott and senior ministers were deeply angry at Barack Obama’s show-stealing climate change speech during the G20. We know because they have been briefing News Ltd columnists to that effect all week – including graphic accounts of how they rang up afterwards and yelled at state department officials for failing to give a “heads up” that the president was going to “dump on” the PM.

Putting aside for one second the extraordinary position we are in when a speech that calls for an ambitious global climate deal and points out Australia has a lot to lose from a warming climate is seen as “dumping” on our prime minister, let’s think about how government ministers could have responded.

They could have tried to defuse the argument – responding to Obama’s call by pointing out that Australia has promised a new longer-term emissions reduction target and will reveal it soon. In fact, as soon as they said that, they also chose to escalate the row with some embarrassingly stupid arguments.

The foreign minister, Julie Bishop, was doing the digging on this one – taking a direct swipe at Obama by saying he and his interior secretary clearly hadn’t read a very excellent briefing provided to them about all the efforts Australia was taking to protect the Great Barrier Reef.

“Of course the Great Barrier Reef will be preserved for generations to come. We don’t believe it is in danger,” Bishop said, with complete certainty.

Perhaps as well as the report about how Australia is attempting to manage the impact on the reef of things like agricultural run-off and shipping activity from the development of enormous coal mines, Obama had also read the most recent report from the Intergovernmental Panel on Climate Change, which says (in chapter 25 - the one about Australasia):

“Recent extreme climatic events show significant vulnerability of some ecosystems and many human systems to current climate variability (very high confidence) … for example, high sea surface temperatures have repeatedly bleached coral reefs in northeastern Australia (since the late 1970s) and more recently in western Australia.”

Maybe the president had read the bit where it said: “Some potential impacts can be delayed but now appear very difficult to avoid entirely, even with globally effective mitigation and planned adaptation” including “significant change in community composition and structure of coral reef systems in Australia, driven by increasing sea surface temperatures and ocean acidification; the ability of corals to adapt naturally to rising temperatures and acidification appears limited and insufficient to offset the detrimental effects.”

Maybe he was making the entirely obvious point that if the world does not continue, collectively, to reduce its greenhouse emissions, the reef will be harmed – no matter what decisions Australia takes about managing domestic impacts.

Even the government’s own “outlook report”, from the Great Barrier Reef Marine Park Authority, found climate change posed the most serious threat reef. Did they not send the president that?

Obama’s $3bn commitment to the Green Climate Fund in Brisbane was a little harder for Abbott to dig himself out of – having previously likened the fund to Australia’s Clean Energy Finance Corporation (CEFC), or “Bob Brown Bank”, which he is committed to abolish (the government recently instructed the CEFC prepare its accounts for the mid-year economic statement on the basis that it will stop making investments on 31 December and cease to exist on 30 June.)

But Abbott could also have said he was thinking about a future contribution, which, Guardian Australia understands, the Department of Foreign Affairs actually was.

But no. Without even a flicker of irony, Abbott and Bishop again dug in further, arguing one reason Australia didn’t intend to commit to the international Green Climate Fund was that it already had the domestic CEFC (neglecting to mention this was only because they haven’t been able to get rid of it yet). They also pointed to the $2.5bn emissions reduction fund – also for domestic emissions reductions and therefore not relevant to the argument, and to foreign aid programs targeting climate mitigation in the Pacific region.

Now that even the Canadian prime minister, Stephen Harper, – the closest thing Australia has to an ally for its climate stance (except maybe Saudi Arabia) – has contributed $300m to the fund, it really seems time to stop digging.

The government points to the fact that Australia met its first Kyoto emissions reduction target – OK, we got a special deal and were allowed to increase our emissions by 8% when everyone else except Iceland had to decrease theirs, but who besides us fact-obsessives is going to remember that? And it insists we will meet our 2020 target, and no one can prove otherwise. Given the task is now only one-third what it was when it set up its Direct Action fund, and given we can “carry over” the extra abatement we got by overshooting our first generous target – who knows, it may even be right.

But the arguments with which Australia is now trying to berate America are truly ridiculous. And they are just drawing more domestic and international attention to our policy absences and inadequacies.

On the domestic front, there’s the truthfulness issue – upon which the last government fell and which appears to be poisoning public attitudes towards this one.

If there is one thing that annoys voters even more than politicians telling lies, it’s those same politicians pointing to previously invisible fine print to try to pretend that they haven’t.

And yet this is exactly what the Abbott government has been doing – over its budget spending cuts and now over its promise not to cut funding to the ABC. It is mounting the entirely untenable proposition that none of this contradicts promises made before the election.

In the case of the ABC it was the communications minister, Malcolm Turnbull, defending the indefensible in the interests of backing in the position of the government.

“Well – well, look, you know, I mean, I’ve defended the prime minister on this today and earlier in the week. I think you’ve got to take his comments, which – look, I mean, what he said, he said, and, you know, it’s there, it’s on the record. But you’ve got to take that in the context. And I can only assume that what Mr Abbott was referring to or was thinking about, anyway, was the proposition that there would be cuts in – with the intent of reducing ABC services and we’ve ruled that out,” he said, not sounding coherent or convincing.

Trailing by 10 percentage points in two-party preferred terms, the government is not short of advice about how to retrieve its political situation as it takes stock at the end of the political year.

According to conservative commentator Andrew Bolt, it has to “change or die”. Some of his advice is probably good – to concentrate on the domestic agenda and to give up on some fights it cannot win. But Bolt also berates Abbott because “he’s given up the fights for free speech and workplace reform, and dares not openly challenge the [global] warming hysteria.” In other words, Bolt reckons the government should dig harder, be more ideological and intransigent.

I disagree. I think it would be better, politically and in the interests of good policy and general sanity, for the government to stop digging for a while.