The government may be forced to push back the next sitting of parliament to enable time for an election recount, following the resignation of another minister on Friday.
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Attorney-General Elise Archer resigned from cabinet and parliament after disparaging messages she sent about colleagues and staff were made public.
The Australian also reported that she was the subject of bullying allegations made by two former staffers in her office.
In the wake of her resignation, Labor Franklin MHA Dean Winter said Labor would not offer the government confidence if parliament resumed as currently scheduled on October 17.
"This is a government that is falling apart, it is disintegrating before our eyes, and I think it's highly likely they will have to prorogue parliament again," he said.
"This is a premier who said that he was going to be strong on workplace harassment.
"He said he was going to be strong on bullying ... and have zero tolerance for these issues, but he's demonstrated nothing of the sort.
Mr Winter said it was disappointing that it took media reporting about Ms Archer's alleged bullying for the government to act.
The state government has delayed parliament sitting days a number of times in recent years, following the resignation of parliament members.
With another member down and a vacant seat before a recount, Labor, Greens and one independent could carry a motion of no-confidence, forcing an early election.
A recount happens when a member of parliament resigns before the term is up.
The Liberal candidate most likely to win the recount is current Hobart City Council Alderman Simon Behrakis, according to political analyst Kevin Bonham.
A spokesman for the TEC confirmed that it won't be possible for a new member to take office by October 17.
"We are currently awaiting formal notice of Ms Archer's resignation, which will determine the timeline," the spokesman said in emailed comments.
Mr Bonham said if parliament resumed with another Liberal member absent, the government would be vulnerable to a catastrophic no-confidence motion, or to attempts to interfere with the government's legislative agenda.
"I think the government would be very silly not to prorogue parliament if they don't have the replacement for Archer in time," Mr Bonham said.
Premier Rockliff said he was seeking advice about the time needed for the recount by the Tasmanian Electoral Commission.
But he acknowledged the threat of a Labor no-confidence motion.
"The Labor Party has been, and will continue to be, a destabilising force within the Tasmanian parliament that is not in the interests of the Tasmanian people," he said.
Whether they launch a motion of no-confidence was up to Labor, Mr Rockliff said.
"We are seeking advice with respect to the timeline of an election of a new member of parliament and I'll make my decision accordingly," he said.
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