Prime Minister Scott Morrison has ruled out accepting a refugee resettlement offer from New Zealand in return for Jacqui Lambie's support on repealing the medical evacuation laws.
Mr Morrison was due to sit down with Senator Lambie on Monday as he courts her crucial support to scrap the scheme.
She has offered to back the repeal bill on one condition but will not say what that is, saying it pertains to national security.
It is believed the condition could centre on the government accepting New Zealand's longstanding offer to resettle some asylum seekers in offshore detention.
Successive Labor and coalition governments have for many years declined to accept the offer, fearing it could send a signal to people smugglers.
"Our policies on those matters haven't changed," Mr Morrison told reporters in Canberra.
The government's Senate leader Mathias Cormann has confirmed the legislation will be voted on this week, even if Senator Lambie's support cannot be guaranteed.
"We will most certainly put the medevac repeal legislation to a vote this week," Senator Cormann told reporters.
"Every individual senator has to make a decision: whether they stand on the side of stronger national security or weaker national security."
The medevac laws, which were pushed through parliament against the government's wishes, gave doctors a greater say in bringing refugees from offshore detention to Australia for medical treatment.
Senate debate on the legislation kicked off on Monday but the final vote isn't expected until later in the week.
Labor's home affairs spokeswoman Kristina Keneally said Immigration Minister Peter Dutton's failure to deliver on resettlement options had led to poor physical and mental health for people in offshore processing.
"Denying people medical care is un-Australian. It is inhumane. It is uncompassionate," she told parliament.
"Labor strongly supports Medevac. Medevac is working as intended. These laws should not be repealed."
Greens senator Nick McKim urged colleagues to block the repeal, arguing decisions on health should be made by doctors rather than ministers or bureaucrats.
"Anybody who does support the repeal of medevac can expect to have blood on their hands," he said.
A loss on the medevac repeal bill could be the government's second significant defeat in as many weeks, after its union-busting legislation was shot down in the Senate on Thursday.
The government sees itself in somewhat of a win-win position on the medevac repeal bill.
If the Senate supports the repeal, the government can claim to have regained control of the borders.
If the government loses the vote, it can continue to attack Labor for supporting the medevac scheme.
Australian Associated Press