Any bid to “fix” the postal survey on same-sex marriage by applying electoral laws to the process may undermine the high court challenge to the vote, Labor and the constitutional law expert George Williams have warned.

The shadow attorney general, Mark Dreyfus, raised the concern in an interview on the ABC’s Insiders program on Sunday in which he suggested the challenge had a 50-50 chance of success and recommitted Labor to pursue marriage equality even if the postal survey returned a “no” vote.

On Friday the Turnbull government first floated the possibility of an urgent bill to apply normal electoral laws to the survey to apply protections against misleading information, fraud, bribery and intimidation.

Labor and the Greens have said they will consider the plan but have still not been provided details of what the government proposes and whether it could extend as far as attempting to prevent hate speech in the debate.

Legislation would have to be brought this week, a sitting week in which the lower house is considering a law to impose new hurdles on aspiring citizens. Labor will also move to refer the postal survey to a Senate committee.

On Sunday Dreyfus said the government, despite saying there would be no hurtful or misleading material “and that they trusted the Australian community and the no campaign to engage in respectful debate, now says it wants to legislate in some way”.

“You might say [the government] should have thought of that before they foisted this ridiculous postal survey on Australians.”

Dreyfus said Labor would “look at whatever the government puts forward” but noted “it might have some consequences for the court case that’s being brought”.

The high court case has listed the challenge to the postal survey for 5 and 6 September, just a week before ballots are due to be mailed out on 12 September.

Williams told Guardian Australia that Dreyfus was “certainly right [because] a key part of the case is that the executive doesn’t have parliamentary support [for the postal vote]”.

“If new legislation expressly or impliedly provided support [for the vote] it could take the wind out of the sails of the challenge,” he said. “[Labor and the Greens] have rejected legislation for the [compulsory] plebiscite. If they want to maintain the strength of the high court challenge, they should exercise caution with whatever legislation might be seen to support the postal vote.”

Asked what Labor would do if the postal survey returned a no vote, Dreyfus said it was “clear Labor policy” that “marriage equality should happen in Australia”.

“We don’t want to be the last country in the developed world to have marriage equality. And we’ll bring it to the parliament after the next election if we’re successful.”

Dreyfus said the high court challenge to the postal survey was backed by “strong arguments” that there was no legislative authority to spend $122m and it was beyond the power of the Australian Bureau of Statistics to conduct the poll.

Asked to estimate its chance of success, he replied: “I’m not going to give legal advice on national TV. Let’s say 50-50.”

Dreyfus suggested the high court could give its verdict immediately after the hearing, preventing any ballot papers ever being mailed out, and supply its reasons later.

The shadow attorney general called on the government to explain which bill for same-sex marriage it would pass if the plebiscite succeeded.

On Saturday the Australian reported that cabinet ministers would “run dead” in the same-sex marriage debate, limiting their activities to stating their position, responding to media questions and encouraging people to vote.

The education minister, Simon Birmingham, however, said he would be doing “everything I possibly can to encourage Australians to vote yes, to support love over fear, to show respect over intolerance”.

“I will be doing everything I can, without distracting from my ministerial duties, to get a yes vote out there,” he said.

The defence industry minister and leader of the House, Christopher Pyne, told Guardian Australia he would “be advocating a yes vote and, assuming I can use my communications budget, [be] writing to my electorate explaining my stance and urging them to vote yes”.

On Sunday the energy and environment minister, Josh Frydenberg, told Sky News he supports same-sex marriage and would encourage people in his electorate to vote yes in the postal survey.

But he said that, when it came to broader campaigning, he had “bigger fish to fry” and energy policy would be his priority in coming weeks and months.

The executive director of the Equality Campaign, Tiernan Brady, said the yes campaign would reach out to 1,300 community organisations, faith groups, unions and corporations to help turn out the vote and fight the campaign.

The Australian Council of Trade Unions secretary, Sally McManus, tweeted on Saturday that the union movement “had the backs” of gay and lesbian Australians and would not be “bystanders to hate”.

Gay & lesbian Australians need to know that @unionsaustralia have their back. We stand up to bullies everyday, we wont be bystanders to hate — Sally McManus (@sallymcmanus) August 12, 2017

A spokeswoman for the acting special minister of state, Mathias Cormann, said the government was still “exploring in good faith how we can complement existing legal protections under current laws” to further ensure a fair process for the survey.

“At the appropriate time all relevant stakeholders will be consulted before we put any proposed bill to the parliament,” she said.