Fairfax Media revealed last week Senator Cormann's offer to work with Labor, the Greens and the crossbench to pass a special law that would ensure the "yes" and "no" campaigns for same-sex marriage were subject to the usual electoral rules, such as protections against malicious publication and bribery.

The law is needed because the $122 million postal survey will be conducted by the Australian Bureau of Statistics, rather than the Australian Electoral Commission, which is subject to the Electoral Act's prohibition on the use of misleading or deceptive material.

On Sunday, Labor's legal affairs spokesman Mark Dreyfus hinted at Labor's support for the special law, saying "our inclination is to make sure that this is a respectful debate".

"If the government won't stand up to the disrespectful and misleading and offensive things that have already been said – we gave Malcolm Turnbull an opportunity in the Parliament last week to condemn for example Bronwyn Bishop's appalling comments. He didn't. If the government won't do that, perhaps we do need to look at other measures."

A senior Labor source confirmed the opposition was very likely to back the bill proposed by Senator Cormann – if a looming High Court challenge to the postal survey failed – but the opposition would only make a final decision once it had seen the proposed bill.

Labor's support would guarantee passage of the law through Parliament.

Senator Cormann told Fairfax Media that "Australians will judge anyone harshly, on either side of the debate, who pursues inappropriate and offensive arguments".

"As we have said, we want this process to be fair and the government is exploring in good faith how we can complement existing legal protections under current laws further.

"At the appropriate time, all relevant stakeholders will be consulted before we put any proposed bill to the Parliament. We call on every Australian to participate in this process with courtesy and respect."

The two High Court challenges – one brought by independent MP Andrew Wilkie, the other by Australian Marriage Equality – challenging the validity of the postal vote will be heard on September 5 and 6.

The parties challenging the validity of the postal survey argue the Turnbull government does not have the authority to appropriate the $122 million in funds for the vote and, further, that ABS does not have the power, under law, to conduct the survey.

Mr Dreyfus said, in his estimation, the challenges had a 50-50 chance of success and the parties were bringing strong legal arguments.

Some of the issues the law proposed by the government could cover include official authorisations applying to printed material, phone calls, text messages, internet and other media – though not TV, as it is already covered.

Broadcasters could be required to provide reasonable opportunities to broadcast material, while bribery, threats and misleading material would all be an offence under the proposed law.

Some legal protections are already in place under existing laws, including for tampering or stealing mail and using the postal service to threaten or harass people, while there are also legal protections from hate speech and incitement to violence under state and territory criminal codes, and the Broadcasting Services Act.

The key dates for the plebiscite are September 12, when the ABS begins posting out ballots; November 7, when responses have to be received; and November 15, when the result will be announced.

Australians have until August 24 to enrol or update their details with the Australian Electoral Commission.