The Morrison government's political fortunes ride on its budget promises of cost-of-living relief and economic recovery, which it hopes will reverse a disastrous lead-in to the 2022 election campaign.

It's no surprise that the loudest voice selling the government's economic credentials has been the ambitious Josh Frydenberg. As the principal architect of the budget and the Coalition's economic message, the Treasurer this year leads what is one arm of the government's two-pronged election strategy.

Heading the charge on the Coalition's other line of attack this election is the equally ambitious Defence Minister Peter Dutton, who has planted himself in the glare of the media this year with a rhetorical bludgeon firm in hand.

His targets have been wide-ranging, both domestic (Labor, for its credibility on national security) and overseas (Vladimir Putin and China).

The latest measures of their media profiles show Dutton, a Queenslander and the most senior member of the Coalition's right faction, and Frydenberg, a Victorian from the centre right, loom large in the Coalition's re-election bid.

Numbers from two media monitors, Isentia and Streem, also show the Defence Minister's presence growing significantly, overtaking Frydenberg on media mentions in February. Dutton's media mentions hit 3500 that month, compared to nearly 2900 for Frydenberg, according to Isentia data.

That probably reflects Dutton's role in a portfolio with a lot happening right now, not least the Russian invasion of Ukraine, a deepening and troubling relationship between Russia and China, and growing tension in Australia's Indo-Pacific neighbourhood.

But Dutton has been forward about making himself heard on these issues, including some that don't fall strictly within his defence portfolio.

The senior conservative's growing media presence serves another purpose, whether he intends or admits it.

If the budget fails to reset the Coalition's election chances, and the government finds no other way to shift the momentum, it could need a new leader after the May election. Even if it wins, Prime Minister Scott Morrison may serve only part-term. That decision may be voluntary or forced by a challenge, depending on the Coalition's fortunes.

Neither Frydenberg nor Dutton, the most likely successors, has sought to hide their ambitions to lead the Liberal party one day. They have also stated their loyalty to Morrison.

"I've made no secret that that would be a - you know, something I'd put my hand up for at the right time. But, you know, we're not looking at that time right now," Frydenberg told the ABC, when asked about his leadership aspirations last month.

Dutton was similarly frank in an interview last November with Newscorp: "I don't think there is any sense in being disingenuous about your ambition and particularly when you've declared it by running in a leadership ballot. It sounds a little lacking in sincerity to suggest that if the opportunity was there in the future that you wouldn't be interested."

Like Frydenberg, he included a caveat. "I don't see Scott Morrison going anywhere anytime soon," he said.

Both Frydenberg and Dutton need to perform strongly this election to seize their chance when the leadership opens up. In an election, as in all politics, that means making the government's case to the public through the media.

Governments have long watched the media mentions of their senior members. Howard government ministries paid attention to it, according to Australian Community Media columnist and former Coalition minister Amanda Vanstone.

A minister's media mentions could reflect something unrelated to them, such as news happening in their portfolio, or a controversy happening at state level. The numbers alone are neither good nor bad, necessarily. They could indicate a minister was under pressure, or performing well.

In the long-term, though, the number of media mentions could reflect something important, Ms Vanstone says.

"Over a long period of time, if you are consistently getting more media mentions, then it does mean that either you're in a portfolio that gets a lot of discussion, and/or you're working hard," she says.

"It's a particular indicator for ministers in portfolios where that portfolio doesn't normally get a high media interest. If a minister holding that sort of portfolio gets higher media, it means they're working very hard."

Frydenberg's media mentions since August have been consistent, and in keeping with the profile of a Treasurer, with spikes around major economic events and updates such as the COVID lockdowns in September and the Mid-year Economic and Fiscal Outlook in December.

Dutton, by comparison, appears to have upped his profile since marking two decades in Parliament with a set-piece interview last year controversially suggesting Australia would support the United States in a military conflict over Taiwan.

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Monash University political scientist Zareh Ghazarian says both ministers would be doing their best to contribute to the government's re-election in the campaign. Life in opposition is a hard slog, especially for MPs used to being ministers in government.

"There is no certainty as to how long, if you lose an election, you'll be out of office," Dr Ghazarian says.

"If these two individuals have political aspirations, they want to remain in power."

Nonetheless, some recent media appearances have raised speculation about Dutton's and Frydenberg's ambitions for the top job.

One image tweeted by Peter Dutton showed him centre stage at a press conference, in the foreground, with the Prime Minister blurred out standing behind him. The image, at the least, appeared disrespectful towards the party leader.

One media report this month also made much of the Treasurer giving "an assertive foreign policy speech that would, in normal times, be reserved for the prime minister". These are not normal times, given the largest European conflict since World War II is unfolding, oil prices are rising, and the pandemic is yet to end. In this environment, the economy and world events are more entwined, and it's appropriate for the Treasurer to speak about them.

The news report also remarked on Frydenberg's "slow cadence" marking the gravity of the moment.

It points to a difference between Dutton and Frydenberg's media presences. Australian National University political marketing expert Andrew Hughes says the Treasurer tended to stay in his lane, speaking mainly about issues of economic performance and management.

Frydenberg's tone is considered and laid back without being casual. His media presence is one of a calm authority, compared to the more provocative and tough-talking Defence Minister.

Dr Hughes believes Frydenberg may fit the national mood better than Dutton. The nation is looking for calm and steady leadership after the tumult of COVID. Dutton's more Trumpian loudspeaker approach, Dr Hughes says, is out.

Judging by the recent Roy Morgan poll, voters respond better to Frydenberg's style. More than 38 per cent of Australians preferred him to lead the Coalition government, ahead of Morrison (31 per cent) and Dutton (12.5 per cent).

Frydenberg was preferred across nearly all key demographic groups including by both genders, by all age groups under the age of 65, in five out of six states and by supporters of the ALP, Greens, Independents and others.

The good news for Morrison is that he is still favoured by Coalition supporters over Frydenberg (47 per cent to 38.5 per cent). Frydenberg seems very unlikely to challenge the Prime Minister. And the election result is far from certain, despite encouraging polls for Labor.

There is another important difference between the Treasurer and Defence Minister, and one Frydenberg might seek to preserve.

Dutton once professed in 2017 that "loyalty is the new black" and went on to challenge a sitting prime minister for the job the next year.

Ms Vanstone says Frydenberg has been loyal to the Liberal party's prime ministers, is a team player, and has not upset the apple cart.

"Dutton has shown his hand in the past, that challenge to Malcolm Turnbull. And now everybody knows that he had then a sense of urgency about taking on that sort of role," she says.

"Now, that didn't work. I'm not sure how that plays out for him in the party room, because when you try things on and they don't work, it knocks a bit of paint off."