Labor wants the minister responsible for the botched census, Michael McCormack, to resign and believes a re-run is not out of the question.
Shadow assistant treasurer Andrew Leigh is furious the government failed to properly explain its decision to take the national survey online, where it was then subject to foreign cyber attacks on Tuesday night.
"If you can't get the census right how can you govern the country," he told ABC radio on Wednesday.
Dr Leigh criticised the coalition for leaving the position of chief statistician vacant for a year and feared it would now blame the bureaucrats.
"What I'm concerned about is that the government is going to pass the buck," he said.
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The shadow minister also warned the quality of the data will be compromised given many Australians were unable to fill out their forms and will have to do it on another day.
"People will, when they go back to fill it in again, have that sense of anger and frustration and maybe they won't be as careful and methodical filling out their census for the second time."
He said the issue of re-running the census was a question worth asking, especially because issues like school funding are based on its data, but it would be expensive.
Dr Leigh urged people to hop online as soon as the website is working again.
Attorney-General George Brandis says the government has been assured by the ABS and the privacy commissioner that census data protections are more than sufficient to protect people's information.
"The Cyber Security Operations Centre has been engaged overnight and is investigating the matter," he told ABC radio.
The Australian Privacy Commissioner opened an investigation into the ABS and its handling of the attack.
"My first priority is to ensure that no personal information has been compromised as a result of these attacks," Timothy Pilgrim said in a statement.
Independent senator Nick Xenophon, who had refused to put his name to the census, questioned how the public still could trust the ABS and its privacy assurances.
He demanded the agency explain where the attack came from and whether it really was an attempted hack or just a system overload.
"I think they need to fess up," he told ABC radio, demanding a Senate inquiry.
