The more difficult political issue is Tony – Abbott, that is.

The former prime minister this week set the scene for a more prominent public role over the next five to six months.

In a series of media interviews and articles and a speech in Singapore he referred to the successes of “my government” and his “leadership”, positioning himself to be a kind of commentator-in-chief.

Abbott was keen to defend the legacy of his government, ranging from the Medicare co-payment to fighting extremists, and boasted that he could have won the next election – although the opinion polls suggested otherwise.

He described his two years in office as the “foundation” on which the Turnbull government is now building and his defence of this legacy can only help the prime minister “to do the right thing”.

Being relegated to the backbench, Abbott will decide on his parliamentary future in April or May next year.

What most strongly struck a chord were his comments on Islam.

The Islamic faith needed to “modernise from the kill-or-be-killed milieu of the Prophet Mohammed”, Abbott said.

Turnbull is unfazed by his predecessor’s insertion into the political debate.

But he offered veiled criticism.

“The one thing we need to be very careful not to do, and I’m sure Tony agrees with this, is play into the hands of our enemies and seek to tag all Muslims with the responsibility for the crimes of a few,” the PM said.

Abbott’s comments were met with raised eyebrows within moderate sections of the Liberal party, and outrage by Labor.

Ed Husic, the only Muslim MP in parliament, said conservative politicians should think more carefully about their words.

“Please … let’s do this in a way we lock arms to achieve this rather than pushing people away,” the Labor MP says.

Abbott’s supporters are concerned Turnbull hasn’t properly acknowledged the former leader’s talents, with some suggesting he should even be considered for a ministry.

It has the hallmarks of a rear-guard action, as conservatives continue to simmer over the disloyalty of their colleagues who dumped Abbott in September.

Former Labor prime minister Julia Gillard found out the hard way that squeezing out Kevin Rudd wasn’t the best idea.

The second challenge facing Turnbull is tax.

As the prime minister was due to meet with premiers for his first Council of Australian Governments meeting, a possible hike in the GST remained lead in his saddlebags.

Labor sees its opposition to any change in the GST as a vote-winner and key point of differentiation with the coalition.

And much evidence has been produced this week that any rise in the rate or broadening of the base would need billions of dollars in compensation especially for low to middle income earners and retirees.

That’s not to mention the impact it could have on the cost of education, health and other essential services.

Having put it on the table, Turnbull and Treasurer Scott Morrison now seem to be tiptoeing away from the GST to focus on other areas of possible reform in cooperation with the states.

Morrison this week said that if the states wanted more GST revenue merely to spend more money on services, rather than cut their own taxes and wasteful spending, he was not interested in talking.

Dropping any change to the GST may ease some political pain, but it will also put pressure on Turnbull to find other ways to solve his budget woes and boost the economy and jobs.

Clawing back tax breaks for high-end superannuants and taking a fresh look at the billions spent on negative gearing of property may reap large benefits, but won’t play well among Liberal and Nationals supporters.

Changes to areas of competition policy have their merits but aren’t easy to explain.

If voters start to wonder about Turnbull’s economic credibility, the government’s current flatlining poll position will begin to track down.

It’s a long bow to suggest the two Ts – tax and Tony – could then converge, with Abbott seeking a return to the leadership to restore the government’s credibility.

But nevertheless it’s a testing time for Turnbull.

– AAP