Prime Minister Scott Morrison says he is "deeply sorry" the Centrelink website and phone system have been crashing and appealed for people, "even in these most difficult of circumstances, to be patient".
Queues outside Centrelink offices have spread to Sutherland Shire following the shutdown of non-essential services, which has impacted the hospitality and many other industries.
"We are deeply sorry about this," Mr Morrison said on Tuesday night.
"I mean, we've gone from 6000 to 50,000 to 150,000 all in the space of, a matter of, a day. And tonight, they're working to boost [Centrelink capacity] again.
"I would say to Australians, yes, we are terribly sorry, but at the same time, we are asking Australians, even in these most difficult of circumstances, to be patient.
"Everyone is doing their best. What we're dealing with is is unprecedented.
"No system is built to deal with the circumstances and events that we are now facing as a nation.
"And I would urge people as difficult as it is, work with us.
"We are working to get this up as high and as far as we can.
"But we have had a multiple, many, many, many times over what is normally expected from this system.
"And it was already upgraded and it's been upgraded again and it will be upgraded again."
Mr Morrison said opening hours for the call centres had been extended and no resource was being spared to ensure the systems were in place.
"But the support is there. It will get to you. And it is dated from when you've expressed that intent," he said.
"And that's all registered and that's taken care of.
"So even if it takes a few more days to get the arrangements sorted out, it will go back to the time from when you needed it.
"And we'll work those, through those issues together and it deeply distresses me as I know it does the Ministers and the Secretary of the Department and all the people who are working there trying to get this as good as they possibly can because they want to get that support to Australians.
"I want to get that support to Australians. And we're going to do our very best to get there."