As parliament gets ready to sit for its final fortnight for the year, Queensland senator Gerard Rennick and South Australian senator Alex Antic have said they would withhold their vote from all legislation unless vaccine mandates are scrapped.
One Nation leader Pauline Hanson has already promised to cause "mayhem" for the government over the issue.
Finance Minister Simon Birmingham said the government would not seek to overhaul mandates.
"The government won't be dictated to, we will do as we've always done, which is work with our health advisors," Senator Birmingham told ABC Radio on Monday.
"What I urge any parliamentarian to do is not to hold one issue to another unrelated issue, each piece of legislation ought to be considered on its merits."
Senator Birmingham said he still respected the right of other government members to cross the floor of the Senate.
"It is a time-honoured tradition of the Liberal National Party ... that we allow our MPs to cross the floor without being tossed out of the party," he said.
"However, it's a right that should always be used sparingly and I would urge any member of parliament to not conflate unrelated issues."
Treasurer Josh Frydenberg said discussions were ongoing with the disaffected senators over their vaccine mandate stance.
"We will continue to present to the parliament important pieces of legislation," he told the Seven Network.
The treasurer said the issue of vaccine mandates were for state governments.
Meanwhile, Opposition Leader Anthony Albanese has accused Prime Minister Scott Morrison of pandering to extremists for not fully condemning violent demonstrators protesting against vaccine mandates.
Mr Morrison had drawn criticism for urging states with mandates to allow freedoms for the unvaccinated, such as being allowed to enter retail and hospitality venues.
"The prime minister should be capable of just showing leadership, not being weak, and saying these comments and this behaviour is unacceptable in Australia in 2020," Mr Albanese told ABC Radio.
"I hold the prime minister responsible for failing to call out unequivocally, the violent and extreme comments that are made, the taking of gallows, the threatening of Labor MPs and premiers and independents."
The government also plans to use the final sitting weeks of parliament for the year to pass its religious freedom laws.
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