Donald Trump "will do everything in his power" to halt the refugee deal between Australia and the US, according to a hardline Texan congressman who is confident no resettlements will ever take place from Manus Island or Nauru.

More than two months after the agreement between outgoing President Barack Obama and Prime Minister Malcolm Turnbull was announced, slow progress on applications and lengthy security vetting by the US Department of Homeland Security is raising fear among those held in the Australian offshore immigration detention centres, ahead of Mr Trump's inauguration on January 20.

Texas Republican Brian Babin, a prominent critic of Mr Obama's refugee resettlement policies, called the one-off Australian deal "madness" and said the incoming administration would overturn it.

A member of the hard-right Freedom Caucus, the two-term representative of Texas's 36th congressional district said Mr Trump would block any of the planned resettlements facilitated by the United Nations High Commissioner for Refugees because of risks to the safety and security of America's citizens.