Labor Senator Deborah O'Neill supported the $84 billion coronavirus stimulus package as it passed Parliament late on Monday night but criticised Centrelink's inability to cope with demand in Wagga.
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Senator O'Neill said the opposition "let it through as quickly as possible" in order that government money would soon reach businesses and unemployed people.
"It is good that it has gone through. We would do things differently if we were in government," she said.
"This is the Liberal Party's package and we wanted to get it out as soon as possible.
"In fact, we worry that it has been too little, too late already."
The stimulus includes a $550 per fortnight supplement to both existing and new recipients of JobSeeker Payment, Youth Allowance Jobseeker, Parenting Payment, Farm Household Allowance and Special Benefit.
The government will also provide two separate $750 payments to aged pension, veteran and other income support recipients and eligible concession card holders after March 31 and July 13.
Eligible small and medium-sized businesses can claim between $20,000 and $100,000 to help maintain cash flow during the pandemic.
Riverina MP Michael McCormack told Parliament on Monday that "Australians, as we all know, are resilient people".
"They will get through this together-we will get through this together," he said.
"This government is working hard every single day and every single night to make sure we get through this unprecedented time, this time of crisis.
"While restrictions on the movement and association of people are necessary, I want to reassure Australians that logistics and supply chains remain in place. There will be no shortage of food for families over coming months."
Mr McCormack said Australia's agriculture industries produced "more than enough to go around" and the supply chain from farms to shops "will not let Australians down".
"As well as our various economic actions to back regional Australians and their jobs and to keep the doors of small business open, the government has set aside a billion dollars for the regions' communities and industry sector, to ensure that those most impacted by the coronavirus will receive the help they deserve and need," he said.
Wagga's Centrelink office saw lines stretch out the door starting early Monday afternoon as new virus containment rules started costing people their jobs.
Centrelink's website also went down on Monday and had intermittent service on Tuesday as hundreds of thousands of people tried to access online welfare services.
"I'm really concerned about what the Centrelink offices images tell us about this government's capacity," Senator O'Neil said.
"They have access to the truth, to the information and the minister Stuart Robert stood up on Monday of all days, when a million Australian logged on to try and get support from Centrelink, the minister said there was a cyberattack.
"That was a lie that he had to correct later in the day. That is just not to the sort of thing that Australians will put up with or should put up with."
Government Services Minister Stuart Robert told 2GB radio he "probably should have waited for the investigation before jumping the gun" and blaming a cyberattack.
Mr Robert also said he had not anticipated the demand on Centrelink after state and federal leaders announced sweeping measures to close public venues on Sunday.
"My bad, not realising the sheer scale of the decision on Sunday night by the national leaders," he said.
"That literally saw hundreds and hundreds of thousands, maybe a million people, unemployed overnight."
Senator O'Neill encouraged anyone having trouble accessing Centrelink or other government services to contact her office.
"I stand ready to help in whatever way I possibly can to hold the government account even though we will not be in Canberra in the usual way," she said.
"My job, as I understand it going forward, is to be the helper that people need when the government fails to respond to their needs.'
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