After Thursday’s announcement that cabinet ministers Linda Burney and Brendan O'Connor were stepping down from the frontbench, all public attention came on to the reshuffle to be unveiled on Sunday.

Behind the scenes, however, something else is preoccupying the government. Ahead of the June quarter inflation figure out on Wednesday, the collective holding of breath is palpable. That number, and its consequences, could affect the government’s political fortunes for months.

The markets expect inflation to increase from the previous quarter’s 3.6% annual figure. If that happens, days of debilitating public speculation will follow, about whether the Reserve Bank at its August 5–6 meeting will raise interest rates or decide, in light of an economy that’s crawling along the ground, to hold them steady.

Australia’s inflation rate has come down from 7.8% in the December quarter of 2022 to the March quarter’s 3.6%. But a turn upwards, even relatively small, would get people worried.

Who’d want the job of bank governor Michele Bullock right now? If rates were hiked in August, Bullock would take a heap of flak. But, unlike the government, she doesn’t face an election. Critics, especially the opposition, would accuse the government of fuelling inflation with its budget cost-of-living measures, although Treasury has estimated they reduce inflation.

The Westpac forecast for the June quarter is an annual rate of 3.8%. Inflation is being fed by rises in petrol prices, insurance and rents.

This week the markets’ expectation of an August rate rise is still relatively low. So for the government, there is an encouraging chance of dodging the bullet – and the ire of home buyers.

On the other hand, the bank has made it clear it won’t be deterred in its fight against inflation. Bullock said after the board’s June meeting: “We need a lot to go our way if we are going to bring inflation back down to the 2–3% target range. The board does need to be confident that inflation is moving sustainably toward target and it will do what is necessary to achieve that outcome.”

The government points out that as inflation falls, it doesn’t necessarily come down in a straight line. However, its earlier expectation (or hope) that by the end of this year inflation could be within the bank’s target range must be in doubt, although Treasurer Jim Chalmers wouldn’t concede that.

An August rate rise would be a heavy blow for the government, but even if that is avoided, the crucial rate fall it is looking for is a long time away. And how much political advantage an eventual single rate decrease would bring is likely limited, after home buyers have faced more than a dozen increases.

The latest Freshwater Strategy poll, published this week in the Australian Financial Review, shows voters in a funk of pessimism, which will take a lot of turning around.

More than half (56%) think the country is headed in the wrong direction; fewer than three in ten (29%) believe it is going the right way. Some 50% say the economy will have worsened a year from now; just over one in five (21%) believe it will have improved.

Meanwhile Sunday’s reshuffle will aim at removing barnacles as well as giving an opportunity for a refresh of the team.

Immigration Minister Andrew Giles is expected to be moved, in an effort to neutralise what has been a fraught issue for Labor.

Giles, a Victorian left winger who was a solicitor for asylum seekers and reacted emotionally to Labor’s 2015 embrace of turning back boats, was always likely to strike trouble in this post. Then the High Court decision forcing the release of a batch of immigration detainees put him into a spotlight that often had him looking near frozen.

There has been speculation his senior minister, Home Affairs Minister Clare O'Neil, may also be shifted. O'Neil’s performance has been lacklustre. Anyway her behemoth department is too large and unwieldy, ranging from cyber security to border control. Administratively, it performs poorly.

What Albanese should do is break up Home Affairs, and elevate the immigration minister into cabinet. But that would be radical.

The obvious replacement for Burney is Malarndirri McCarthy, assistant minister in the Indigenous portfolio, who was formerly a member of the Northern Territory parliament. It would be a big step up for her, in an area where Labor appears to have lost its way since last year’s failed Voice referendum.

It’s hard to avoid the conclusion the government in recent months hasn’t wanted Indigenous affairs policy to the fore, especially in the run up to the August Northern Territory election. Or perhaps it simply hasn’t been able to work up a plan. The referendum left the government dispirited and with a vacuum, and Burney exhausted.

A changing of the ministerial guard does (or should) provide an opportunity to draw a line under the referendum debacle, and embark on a policy refresh.

Late next week Albanese will attend the Garma festival in northeast Arnhem Land. Garma is far more than a cultural gathering. It is an occasion that brings together Indigenous leaders, as well as politicians and others with a stake in or connection to Indigenous affairs.

One attendee this year will be Danielle Wood, the head of the Productivity Commission, which next week will release its latest update on the Closing the Gap results. It doesn’t take that report to tell us that on many fronts, the gap is yawning.

Aboriginal and Torres Strait Islander policy is one of the Productivity Commission’s new policy areas of focus; it will be consulting on a research plan in coming months.

The commission is not the only specialist economic player working in Indigenous affairs. The Treasury also has a unit devoted to this policy area. Chalmers himself is taking an increasing interest.

The involvement of economic departments and agencies is vitally important to achieving progress, for a couple of reasons. One is that the bureaucracy supporting Indigenous policy hasn’t been nearly as strong as required. Another is that if communities could be given a lot more economic sustainability, that could help alleviate (albeit not solve) some of the social problems.

As things stand, if he disappeared off the scene today, Albanese would have only a failed legacy in Indigenous affairs. He needs to use the months ahead and (assuming) a second term to turn that into some substantial positive achievements. We know from history it won’t be easy.