In Newspoll's second round of state Premier approval ratings, Mr Gutwein achieved a net rating of 82 per cent and satisfaction rating of 90 per cent.

This is up from the first round in April and according to political analyst Kevin Bonham is the highest satisfaction rating in any scientific opinion poll in Australia ever, beating out an 89 per cent satisfaction rating previously held by Western Australia Premier Mark McGowan.

The senior Labor source, who did not wish to be named, has speculated this would put additional pressure on the leadership of Ms White.

The source said despite Mr Gutwein's high rating, the Liberals may not do as well as expected in the Legislative Council election for Rosevears because Tasmanian voters understood their electoral system and valued independents in the upper house.

Former The Examiner deputy editor and Liberal advisor Barry Prismall said he did not think the Premier's popularity reflected negatively on Ms White and if she had been Premier she would have similar ratings.

"It's a really tough gig to be in opposition at the moment because you are sidelined," Mr Prismall said.

"Early in the piece Labor starting attacking Morrison federally, and now they've started attacking Gutwein in Tasmania - they are damned if they do, damned if they don't."

Mr Prismall said Mr Gutwein had performed well by showing resolve, compassion and empathy through the COVID-19 crisis.

"I'm not disparaging the seriousness of the pandemic [but] it's fortuitous for him that when he took over from Will Hodgman there was a pandemic which has enabled leaders across the country to shine," he said.

"With National Cabinet, they've got the best of the best in Australia giving them advice on what to do and they are all basically agreeing with it. It's pretty hard to make a blunder.

"Once it's over and they go back to politics and the hum-drum of it all, Gutwein's approval will probably go back to normal levels of 50 or 60 per cent."

He said Labor should not be too discouraged heading into the next state election in 2022.

"It would be folly for anyone to say Gutwein's got it in the bag before the next election," Mr Prismall said.

"A week is a long time in politics."

Mr Gutwein's popularity would not do any harm to the Liberals' Rosevears candidate Jo Palmer, Mr Prismall said.

"She's pretty well-known anyway. I suspect it may help her get over the line," he said.

When asked if she was concerned about Labor's position given Mr Gutwein's high approval rating, Ms White said Australia's response to COVID-19 had been extremely effective and this was reflected in high approval ratings for leaders, particularly in states that have successfully suppressed the virus.

"Labor is firmly focused on ensuring that people are not left behind as we move to recovery from COVID-19," Ms White said.

Mr Gutwein's continued popularity has again prompted speculation the government may head to an early election but Deputy Premier Jeremy Rockliff said the government had no plans to bring forward the vote.

"There's too much to do. Tasmanians expect us to get on with the job," Mr Rockliff said.

"Yes, [the Premier] has done a wonderful job we are not focused on polls, we are focused on rebuilding the economy."