Health Minister Michael Ferguson remains upbeat despite Liberal colleague Sue Hickey urging him to stand aside and Labor trying to move another no-confidence motion in him.
The Opposition seized on comments made by Ms Hickey that Mr Ferguson should reconsider his position as Health Minister which he has held for five years.
For the second day in a row in State Parliament, Labor tried to suspend parliamentary business to debate a no-confidence motion in Mr Ferguson.
The motion to suspend standing orders failed to win the required two-thirds majority for a debate to proceed.
Ms Hickey said later that she would not have supported a motion of no-confidence "at this point in time".
"I'm not sure what Labor's tactics are bringing it up in the method they have been doing because it must require a two-thirds majority so they're going to fail every time," she said.
She said Mr Ferguson was "doing the best he could" but a "fresh set of eyes" might help.
"Michael Ferguson's a very competent minister and he's actually a really nice guy when you get to know him," Ms Hickey said.
"He probably sometimes comes across as a bit arrogant which might be a self protection mechanism.
After her criticism on ABC radio, Ms Hickey toned down her call for him to stand aside and said he needed an assistant minister or "a break".
"Michael Ferguson came to see me and he's happy to work with me going forward - he's very keen to ensure I'm at the next round-table summit, although I intend to just go and listen," she said.
"I'm not certain of anyone lining up for his job, I think they might have to be pushed into his job."
During question time Labor leader Rebecca White asked Mr Ferguson: "Will you finally do the right thing and finally put the health of patients and the welfare of staff before yourself and resign?"
Mr Ferguson said he had the "strong support of my colleagues"
"I feel very grateful for the honour of performing a very difficult job as the Health minister, a job that members opposite did not even want," he said.
"We relish the opportunity to work to provide Tasmanians with a better health system.
"I reject any suggestion that the government does not enjoy good and professional working relationships because those relationships have enabled significant reforms that have led to improvements in our health system."
The Opposition's latest no confidence in Mr Ferguson cited 17 reasons including ambulance ramping and lack of abortion services.
Deputy Labor leader Michelle O'Byrne said Mr Ferguson was a "dead man walking" ahead of his health round-table next week.
Deputy Premier Jeremy Rockliff said Mr Ferguson was someone who listened.
"He wakes up every single day and wants to help with the challenges in the health system," Mr Rockliff said.
"This is just a re-run of the stunt yesterday."
Greens health spokeswoman Rosalie Woodruff said the no-confidence motion needed to proceed so each member of the government could speak in defence, or otherwise, of the minister.Ms Hickey had told ABC radio on Wednesday morning that it was time for Mr Ferguson to consider his position.
"He's lost the faith of the doctors, he's lost the faith of the nurses, there's not a lot of faith in the parliament," the Liberal member for Clark said.
"You know he just stands up every day and says 'thanks for this report, thanks for that report', some of the most damning reports I've ever read."
Ms Hickey said a letter from nurses to Mr Ferguson - the subject of Labor's unsuccessful motion on Tuesday - made her feel sick.
"We as Liberals cannot go on another day in this Parliament saying 'it's all your fault' across the table," she said.