It's hard to forget the intensely awkward image of Tony Abbott offering comfort to a seemingly forlorn Joe Hockey ahead of the 2015 budget.

What was intended to be just one of those run-of-the-mill, stage-managed shots unintentionally became an extraordinary insight into the deep funk of the Abbott government.

In hindsight, it was a glimpse into the political gallows.

A prime minister, himself just weeks from having escaped a self-declared "near-death experience" at the hands of appalled colleagues, was appealing to his treasurer to be their collective saviour.

In that instant, Tony reached for Joe's arm, as if to cajole him for one more big effort before the show started.

"C'mon, it'll soon be over," he was telling the dispirited treasurer, when he knew it had only started.

It was perhaps about this time when the then-PM realised that the bloke he once decked at Sydney University rugby scrumming session wasn't the man mountain he'd hoped. This fella wasn't up to it. Joe was spent.

Both men were little more than four months from the end of their ministerial careers.

But it was the budget that came the year before that did them both in.

The 2014 budget lethally wounded Mr Abbott and Mr Hockey.

It defined them as either ideologically off-key with the driving force of the Australian political centre or shockingly tin-eared. Or both.

The first budget of the Abbott government remains a familial disgrace for the Liberal Party.

It was a budget that was seen to have failed the fairness test and three years on, the Coalition is still dealing with its fallout.

Even though Tuesday's budget is Scott Morrison's second as treasurer, its major task will be finally dealing with the Hockey "nation of lifters, not leaners" legacy stain.

Mr Morrison's first budget last year was too soon from his taking of the treasury portfolio in September 2015 and too close to the looming election for much of the necessary reconfiguration.

So for three years, $80 billion of combined cuts to schools and hospitals have sat on the books, putrid and unloved, along with a savage 20 per cent cut to university funding.

Scott Morrison has some serious spruiking to do on Tuesday.

As much as Mr Morrison's budget on Tuesday must answer the fairness question first and foremost, his other top priorities will be to show a new way on education and health.

This is an imperative for the Coalition because of Labor's superiority on both issues.

The Coalition will not be able to out-spend the ALP in promises on health or education — that's the advantage of Opposition, for a start — but nor can it afford to allow Labor to go unchallenged on either front.

Mr Morrison has two critical Cabinet conscripts in this regard: Education Minister Simon Birmingham and Health Minister Greg Hunt.

These ministers will be playing very significant co-starring roles in the budget in their bid to extract the coalition from twin political ills.

Senator Birmingham made big inroads with his task this week, first with his rejigged reforms for the university sector and then the outrageous repurposing of Julia Gillard's schools tsar David Gonski.

How better to do that than stealing Labor's talisman-hostage and embracing his needs-based, sector-blind school funding model?

This is smart politics but not without hazard.

The Catholic sector's furious response was predicted by the Government, insiders say, but will nonetheless require very careful navigation.

Because as Prime Minister Malcolm Turnbull has so often found, his internal critics are skilled at fanning discontent through proxies.

And sectarianism is a dangerous propellant, even if the Catholic archbishops, as the Government whispers, are simply showing resistance to greater transparency.

But if Senator Birmingham can deliver the decade-long schools funding regime that he promises, Opposition Leader Bill Shorten will lose one of his sharpest 2018 campaign sabres.

Labor will be worried by the Greens' apparent mood for settlement of the schools funding debate.

Mr Hunt is similarly focused on a long-term coalition conciliation with his area of responsibility.

He has spoken of four pillars in health: Medicare; hospitals; mental health/prevention; and research.

Like his colleague in education, Mr Hunt's unspoken task is to close down Labor's advantage.

And like education, the health budget is still awaiting formal adjustment from the over-reach of the 2014 budget.

The $5 co-payment, a $1-billion zombie saving that has haunted the books since Peter Dutton's days, will finally be put to rest.

The various Medicare co-payment freezes, some begun under Labor, will be progressively thawed, beginning with concessional GP visits from July 1, general patients and specialist consults in 2018 and specialist procedures in 2019.

And as 7.30 explored this week, significant savings from the Pharmaceutical Benefits Scheme will be ploughed back into listing new drugs.

The budget will provide some useful hints towards the next hospitals agreement, though this won't be finalised until next year.

Fairness and reconfiguration of the health and education settings will be the three necessary pillars of the budget.

And if Mr Morrison succeeds on Tuesday night, know that in large part it will be because he has exorcised the ghosts of budgets past.