The state government has been in minority since May when Lara Alexander and John Tucker left the Liberals to sit as independents.
They cited concerns over a deal for an AFL team and new stadium, but signed a written agreement to provide votes of confidence and supply in parliament.
Mr Tucker last month threatened to move a no-confidence motion in the government when parliament resumes in March if animal welfare oversight in abattoirs isn't improved.
Premier Jeremy Rockliff has written to the pair, accusing them of having a "my way or the highway" approach.
"I will accept genuine cooperation that is in the best interests of Tasmanians, but I will not allow the government to be held to ransom every sitting week," he wrote.
Under the proposal, Mr Tucker and Ms Alexander would be barred from supporting Labor, Green or other independent bills or amendments without government approval.
They would provide confidence and supply except in instances of corruption and malfeasance and keep the right to bring forward motions and bill amendments of their own.
"If we are unable to reach a new agreement prior to the resumption of parliament ... I will be forced to consider all options, including potentially advising the governor to dissolve the house," he said.
The next state election isn't due until mid-2025 but both the Liberals and Labor opposition have announced candidates in recent months.
The Jacqui Lambie Network has also announced it will run candidates in several seats.
Ms Alexander told the ABC she could not support a new deal that prevented her from supporting motions or amendments from other parties.
However, she also hoped a "path forward" could be found.
"It's a mockery. It goes against the grain of being an independent," she said of the premier's proposal.
"If something is good, why should I not support it?."
Mr Tucker has indicated he is considering his position.
Labor Opposition Leader Rebecca White said the only way to "end the madness" was an early election.
"It's clear that Jeremy Rockliff has lost control," she told reporters.
"His weak leadership was the reason the two backbench members deserted him in the first place, citing concerns about integrity and transparency."
Tasmania's lower house of parliament is increasing from 25 seats to 35 at the next state poll.
According to the most recent voter opinion poll, neither major party would be able to win enough seats to form government in majority.
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