Health Minister Bridget Archer will be acting Tasmanian premier for about a week from tomorrow while Jeremy Rockliff and his deputy Guy Barnett are away.

The announcement was made with little fanfare at a Tuesday morning press conference.

This particular moment in the craziness that is Tasmanian politics may seem inconsequential to those who don't live and breathe the stuff.

But make no mistake, this is significant.

This is a trial for Mr Rockliff's pick for the next premier of Tasmania.

And the decision to install Ms Archer in the top job, even for the briefest of periods, will set tongues wagging and no doubt turn some within her own party green with envy.

It's been just under a year since Ms Archer was elected to state parliament, after unexpectedly losing her federal seat in Labor's landslide.

During her time in federal parliament, Ms Archer became known nationally for speaking her mind, even if that meant criticising her own party.

She crossed the floor a total of 28 times on issues such as religious discrimination, integrity and climate change — possible only because she was a backbencher.

But as a senior minister in the Rockliff government, Ms Archer has found herself having to deal with and defend the state's broken health system.

Health is known as the poisoned chalice for a reason, and she is an easy target in Question Time as she fields questions about patients getting taxis to hospitals and ambulance waiting times.

Most recently, she's been forced to defend the government's $700 million of cuts across the health system — stuck in a bizarre argument with Labor about whether there are cuts or not.

For the record, both parties are a bit right — health spending is growing year on year, but they also need to find $700 million in efficiencies across four years, aka cuts.

It's all about semantics.

Ms Archer may no longer seem like the outspoken Liberal MP that Tasmanians remember from federal parliament, but that is the reality of being a minister.

When pushed in parliament by Labor recently on the health cuts, who highlighted her record of crossing the floor, Ms Archer fired back.

"I have made an entire career of standing up for things that I believe in," she told parliament.

"You can bet your bottom dollar, if I'm not standing up and saying that now, it's because I believe it.

"It's because I believe that we need to make efficiencies to protect the wellbeing of future generations."

Archer on 'Team Tasmania', says Rockliff

Mr Rockliff has never been shy about his admiration for Ms Archer.

She is, after all, much like him, a traditional small 'l' Liberal, strong on social issues — like when the pair defied then-federal Liberal leader Peter Dutton and campaigned for the Voice — and a believer in small government.

Before the Tasmanian governor had even granted Mr Rockliff his 2025 election request, he was out declaring that Ms Archer would be running in Bass.

Months later, when Mr Rockliff was re-elected, ahead of the second — this time destined to be unsuccessful — no-confidence motion, Mr Rockliff hosted a brief press conference outside parliament.

He was flanked, not by his deputy or treasurer, but by close ally minister Jo Palmer and Ms Archer.

Even then, it appeared a sign of things to come.

But the key thing to remember is that Ms Archer is the premier's pick, not the Liberals'.

While there are still a significant number of moderates in the parliamentary Liberal Party, the ones with power are largely the conservatives.

Think Treasurer Eric Abetz with his more than three decades of parliamentary experience, the state's deputy premier, Guy Barnett, the next generation's conservative hope, Police Minister Felix Ellis and even former deputy premier Michael Ferguson, biding his time on the backbench.

All of whom have been in the state parliament longer than Ms Archer, and all are known to harbour leadership ambitions.

It's no secret some were doing the numbers when Mr Rockliff faced his first no-confidence motion last year.

And there is certainly no love lost between Ms Archer and fellow minister Gavin Pearce, who reportedly tried to pressure the federal Liberals to dump her when he held the federal seat of Braddon.

Should the Liberals install their first-ever female premier — and the state's second — it might not be easy going for her.

Australia has just witnessed the bloodbath that was the federal Liberals' first female leader being torn down by her own party within a matter of months.

Strategic succession

So how could Ms Archer even take over, given how many MPs could argue they are in line before her?

Well, there are two points in her favour.

Firstly, her impressive performance at the ballot box, where she topped the poll in Bass and received almost double the number of votes as the next best placed Liberal, Michael Ferguson.

And secondly, Mr Rockliff would likely argue she is the only person the largely progressive crossbench will accept.

While there might not be an election on the horizon anytime soon, the Liberals' hold on government is rather tenuous.

They are in power not because the crossbench and the Greens are particularly fond of them, but because last year they were viewed as the lesser of two evils.

But under the leadership of Josh Willie, Labor has changed.

There is less antagonism towards the Greens and more of a willingness to work together.

While it's been slow going, things between the parties are thawing.

The recent team up to kick two government ministers to the backbench seems to have warmed things even more.

The Liberals are not the natural partners of the Greens or most members of the crossbench, but they tolerate them, in part because of Mr Rockliff himself.

They certainly have their issues with him — just look to the integrity concerns the Greens raised last month — but his stance on things like greyhound racing and equality still commands respect, as does his general decency.

Premier Eric Abetz or Premier Felix Ellis would probably be a bridge too far for the Greens and independents like Kristie Johnston and David O'Byrne.

Premier Bridget Archer, on the other hand, would be much more palatable, and perhaps the only chance of preventing the Greens and crossbench from installing Labor.

The irony, of course, in all this is that in triggering last year's election, Labor has handed Mr Rockliff and the Liberals their best chance of staying in power longer.

Rockliff keen to keep a moderate in charge

The Liberals are a broad church, and it is their moderate wing that has kept them in power in Tasmania for so long.

It's no secret that when premier Peter Gutwein left, he ensured his moderate deputy in Jeremy Rockliff was ready to take the leadership.

Until now, Mr Rockliff has not had an obvious successor when it comes to finding someone who matches his values.

Perhaps reluctant to leave the state in the hands of someone so ideologically different to himself, he's shown no signs of being ready to hand over the crown.

But after almost a quarter of a century in politics, endless elections, a no-confidence motion and, not to mention, the recent integrity issues and loss of two ministers, it would be understandable if he was planning an exit at some point.

If Ms Archer decides she wants the top job, it'll take a weight off Mr Rockliff's shoulders.

But it'll add a hell of a lot to her own.

The maverick MP has built a reputation over the years of being a frank speaker with strong values, and her progressive stance on social issues has won her fans across the political spectrum.

Even if Tasmanians are willing to accept Ms Archer as premier, the question is: will her own party?