Independent MP Cathy McGowan has asked constituents to help decide whether she should vote for new laws to fast-track medical treatment for refugees on Manus Island and Nauru, in a fresh sign the Morrison government has a chance of avoiding an historic defeat on the floor of Parliament.

The push to give doctors more say in whether sick refugees should be flown to Australian hospitals was widely thought to have the numbers in December after Labor and nearly all crossbenchers indicated they would back it.

Cathy McGowan with Prime Minister Scott Morrison Credit:Alex Ellinghausen

The bill will come before Parliament when it returns in February and presents a risk to the Morrison government's control of the House of Representatives.

But Ms McGowan, who will not recontest this year's federal election, told The Sydney Morning Herald and The Age earlier this week that she had not decided whether to support the bill.