Nasrin Haque and her husband, Shafiqul Bhuiyan, are being deported - despite the fact Dr Haque has been an Australian resident for eight years - because their daughter is considered "too burdensome" for taxpayers, the Australian Medical Association's NSW branch said on Thursday.

"The fact that an Australian resident of eight years, whose parents and siblings live here, can be faced with deportation due to illness is reprehensible," AMA NSW president Brad Frankum said in a statement.

AAP understands the family of four was due to be deported on Thursday but given a two-day extension to purchase plane tickets and show them to the immigration department.

A department spokesman said Assistant Immigration Minister Alex Hawke would only intervene if he thought it was "in the public interest to do so".

"The minister cannot be compelled to exercise his powers and he is not required to explain his decisions on any case," the spokesman said in a statement.

"The minister only intervenes in a relatively small number of cases which present unique and exceptional circumstances."

Professor Frankum says the issue is of immense public interest especially to Dr Haque's community of Pitt Town.

"I would suggest her patients would argue with that," he said.

Federal MP for Macquarie Susan Templeman wrote a letter requesting Mr Hawke's urgent intervention earlier this month, the Seven Network reports.

Ms Templeton stated in her letter the GP "goes above and beyond" her duty, working weekends and providing out-of-hours care for her patients.