The independent MPs behind the push to move refugees off Nauru and Manus Island for medical treatment have demanded Labor hold the line in supporting the proposed law as Bill Shorten ponders a politically safe compromise.

Kerryn Phelps, the independent MP for the Sydney seat Wentworth, said it would be “enormously disappointing” if the opposition backed down, while independent senator Tim Storer said voters might wonder what Labor stood for.

“If Labor does back down now, voters may wonder about the value of its commitments more generally and wonder whether what Labor says before the election is what it would actually do if it comes to power,” Senator Storer said.

Any softening by Labor would represent a significant win for the Morrison government, which was facing an historic defeat in the House of Representatives this week as Parliament resumes for the year.

The current bill before Parliament, which has been the subject of an intensifying political struggle between the major parties, would give doctors and a separate medical advice panel established by the government the power to order the transfer of needy refugees to Australia.