On Monday, Tasmanian Labor health spokesperson Anita Dow said not enough had been done to improve services at the hospital.

"In the budget that was handed down a couple of weeks ago, there was only $50 million for this project when it's actually a $580 million project," Ms Dow said.

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That $50 million spend will be spread out over the next four years to progress stage two of the hospital's upgrade, which includes the construction of a mental health precinct.

"We want to know when the government intends to fund the LGH and when people can expect to see improved services."

Ms Dow went on to bring attention to the hospital's ongoing ramping and capacity issues, which forced staff to turn away some patients at the emergency department in recent weeks.

"Only last week, Northern and North-West Tasmanians were being asked to travel to Hobart to access specialist mental health services because they weren't available in the North and the North-West because of COVID and staff shortages" she said.

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Ms Dow said the state's health system was heading into a "perfect storm" given the expected rise of COVID and influenza cases leading into winter.

"We want to know what the government's backup plan is to provide services and to support our staff through the winter."

When asked what she would like to see put in place as a "backup plan", Ms Dow did not outline any specific initiatives.

In response, the state government pointed to its existing Winter Strategy, which was launched earlier this year. The strategy aims to increase flu and COVID vaccination rates - in an effort to ease demand on hospital services - as well as expand the COVID@home and community case management facilities.

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Premier Jeremy Rockliff said the strategies had already proved "highly effective in managing COVID-19" given the state's low rate of COVID-related hospitalisation and deaths compared to the rest of the country.

"We are confident that bolstering these tried and tested methods and supporting our primary care providers will enable us to deal with the return of flu and the continued presence of COVID," he said.

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