A poll finding a slim majority of Australians support the death penalty for Australian drug traffickers – seized upon by the Indonesian government to justify the killing of Andrew Chan and Myuran Sukumaran – is crude and misleading, according to critics.

The "snap" poll by Roy Morgan Research was conducted in January by sending an SMS to the company's database of people it had previously interviewed, an uncommon method.

But what has most concerned pollsters and lawyers for Chan and Sukumaran is the question that was asked, and the ones that were not.

Morgan asked: "In your opinion if an Australian is convicted of drug trafficking in another country & sentenced to death, should the penalty be carried out?"

Those contacted were asked to reply Y for "Yes" and N for "No".

Just over half of the 2123 people respondents, 52 per cent, replied by typing "Y" on their phones.

Commissioned by Triple J's Hack program and released by Morgan under the headline "Australians think Andrew Chan and Myuran Sukumaran should be executed", the poll has been a devastating setback for the team trying to save the men from a firing squad.

It has received widespread coverage in Indonesia and been repeatedly cited by its ministers and diplomats.

Announcing that the heroin smugglers will be among the next group to be executed, Attorney General H.M Prasetyo said: "We have heard that many Australians support the execution and it is one of the things that pushes us to feel we are not making a mistake."

Indonesia's ambassador in Canberra, Nadjib Riphat Kesoema, meanwhile, said: "We can say that 52 per cent of Australians support Indonesia's position."

Lawyer for the men, Julian McMahon, said the poll result "is now a tool being used to get my clients killed".

"It's so irresponsible," he said. "The AG and the ambassador have publicly relied on the SMS poll as a factor justifying execution. They say that it pushes them to do it, that they have Australian public support."

According to former Fairfax pollster John Stirton, polling about the death penalty has to be handled carefully.

He pointed out that the question posed by Morgan was an "in-principle question". In contrast to the headline on its press release, the question did not ask about Chan and Sukumaran's case directly.

"This issue is very complicated and has many different layers. Asking additional questions will help understand those layers," he said..

"If you asked a follow-up question that referenced Chan and Sukumaran; if you asked 'what if the offence would only carry a few years in prison in Australia'; if you asked 'what is your position if the person is rehabilitated'.

"Well, you will get different answers."

The most recent survey prior to the Morgan poll was conducted by Nielsen on behalf of Fairfax in August 2010, when another Bali Nine member Scott Rush was also on death row. .

Conducted by telephone, it asked: "Three Australian members of the 'Bali Nine' drug smuggling ring have been sentenced to death in Indonesia. Do you support or oppose the death penalty in this case?"

Only 28 per cent answered that they supported the death penalty, while 67 per cent said they opposed it.

Gary Morgan, executive chairman of Roy Morgan Research, defended the SMS poll's methodology, saying it had been used to correctly predict the Queensland election result, and was "the most accurate" of all the election eve surveys.

"We measure public opinion, we don't make public opinion," he said.

"We asked an in principle question because we had a history of asking the same question. It showed the public opinion had hardly changed at all since 2009 [when it was last asked]."