Malcolm Turnbull’s rhetoric this week has been designed to put the heat on Labor over budget repair. But he has three grassfires on his hands even before the new parliament starts on August 30 – and they’re all on his own backbench.

The issues are very different: pressure for action against the banks; bitter objections to the budget crackdown on superannuation tax concessions; and a new push against section 18C of the Racial Discrimination Act.

The common thread is the difficulty they present for a leader who is embattled despite just winning an election. Interviewed by 3AW’s Neil Mitchell on Friday, Turnbull was confronted with questions about each of them.

He hinted there would be something done on the banks, as he tries to defuse the potency of Labor’s campaign for a royal commission.

Backbenchers led by Liberal Warren Entsch and the Nationals’ John Williams want a tribunal that would give victims of bad behaviour a path to redress without an expensive legal process.

“The government is certainly looking at that,” Turnbull said, while pointing out there is already a financial ombudsman. “In terms of improving the way customers and particularly retail customers are dealt with, we’re very open to looking at action,” he said, distinguishing such “real action” from a long and costly royal commission.

The government has clearly got the message that it needs to do more than haul a few bank executives before a parliamentary committee, which was Turnbull’s earlier response. The question now becomes the form of what is done – a new structure or beefing up what’s there.

If the government agreed to a tribunal, it wouldn’t kill Labor’s campaign for a royal commission but it would appease backbenchers concerned about how ordinary people have been hurt, and limit the political damage Labor could do with its proposed parliamentary motions.

The revolt over superannuation is trickier. Liberals up in arms include vocal conservatives such as Eric Abetz and Kevin Andrews; the argument goes beyond the substance to the anger of donors and others among the party faithful.

Before and since the election senior government members have sent out contradictory signals about how much recalibrating of the super measures might be contemplated – from hardly any to a lot. Well-placed sources play down the likely extent of them. Meanwhile, Turnbull told Mitchell “our policy is the one we took to the election”.

Treasurer Scott Morrison has been on a roadshow to talk with MPs this week, as the government tries to juggle the party internals with budget imperatives and its credibility with the public.

On the one hand, the rebellious MPs can make trouble in the partyroom. On the other, if the government retreats on its plan, which is directed at the highest income earners, it doesn’t just lose revenue but undermines its claim that it is sharing around the pain of budget repair.

Of the three issues on which there is dissent, the push from the right inside the Liberal Party and more generally to revisit Section 18C of the Racial Discrimination Act – which makes it illegal to “to offend, insult, humiliate or intimidate” on racial grounds – is potentially the most corrosive for Turnbull in the longer term. It goes to ideology and has become a core issue for many of the anti-Turnbull Liberals.

Critics of the section, who at a minimum want offend and insult removed, see themselves as standard bearers for free speech.

Tony Abbott had to back away from change, under attack from ethnic communities and the Jewish lobby, and because he desired to restrict hate preachers. A week ago Abbott said perhaps his attempt to reform Section 18C would have fared better if it had been more modest. His judgement now is that “as things stand, there’s no real prospect of change”.

Nevertheless, a small but seemingly growing number of Liberals are gearing up for a fresh battle, in which they have crossbench allies in the Senate, including Family First’s Bob Day and Liberal Democrat David Leyonhjelm.

The government’s position is that inherited from Abbott – changing 18C is off the table. But Turnbull on Friday used the wording that it was “not a priority” which, interestingly, left just a crack for the rebels in their slow-burn campaign.

Turnbull brings some baggage. A Daily Telegraph report this week claimed, on the basis of anonymous Liberal MP sources, that indications had been given as part of Turnbull’s campaign for the leadership that he would revisit 18C.

And Day gave The Australian a very specific account of his dealings with Turnbull, who wanted him to delay his private member’s bill to change 18C. Day said Turnbull rang him soon after becoming prime minister and “we landed at the position where I would not put it to a vote, but would bring it back in the new year and we agreed with that timetable”.

Other developments are putting the spotlight on 18C. A decision is coming soon in a court case which a Queensland Indigenous university administrator brought over remarks three students posted on social media after they were asked to leave a computer room reserved for Indigenous students. A ruling in favour of the case continuing would give impetus to those who want 18C changed.

There is also a well-publicised complaint that Leyonhjelm has lodged with the Human Rights Commission against Fairfax journalist Mark Kenny for calling him an “angry white male”.

There will be private members’ bills in the new Senate sponsored by Day and Leyonhjelm and dissident Liberals to change or scrap 18C. They will have no chance of passing.

But if momentum picks up over the issue in the party it would be trouble for Turnbull, who could be caught between vociferous backbenchers and a renewed and likely ferocious campaign of opposition to change from ethnic communities. There would be no way of coming out with a win from that situation.

It’s not just Labor that is determined to play tough with Turnbull in this term.