Mr Biden named Bruce Reed his deputy chief of staff on Tuesday. Mr Reed has been a longtime advisor to Mr Biden and served on his staff during the Obama administration.
Mr Reed was the executive director of the Bowles-Simpson fiscal commission during Barack Obama's presidency.
The bipartisan commission was formed in response to worries about government spending and the nation's growing national debt.
The group recommended significant cuts to the military budget, increasing the federal gas tax by 15 cents, raising the retirement age to 69 by 2075, cutting 200,000 federal jobs, and reforming – making cuts – to Social Security and Medicaid, among other suggestions.
A petition launched by the Justice Democrats to urge Mr Biden not to pick Mr Reed was circulated prior to his selection.
"Joe Biden must not repeat Obama’s mistake. We need our government to spend money now – to ensure vaccines are distributed, to keep people in their homes, to prevent small businesses from closing permanently, and to make sure Americans can stay home until the vaccine arrives!" the petition says.
The petition also points out that Mr Biden and Senator Kamala Harris ran on promises to expand Social Security.
Alex Lawson, the executive director of Social Security Works, an organisation focused on protecting Social Security, issued a statement opposing Mr Reed's selection.
"During the worst national crisis since the Great Depression, the last thing we need are Social Security cuts – or any other form of austerity," he said. “We are extremely disappointed by this selection, which is inconsistent with President-elect Joe Biden’s campaign promise to protect and expand Social Security benefits.”
Mr Lawson continued by pointing out that Mr Biden has made better selections, and that his administration should avoid austerity measures.
Mr Biden's platform included increases to Social Security.
Under his plan, eligible workers would be guaranteed a minimum benefit equal to at least 125 per cent of the federal poverty level. Individuals who have been receiving benefits for at least 20 years would also get a 5 per cent bump. Widows and widowers would also be given an additional 20 per cent per month.
After leaving Mr Biden's staff, Mr Reed led a foundation for one of the nation's largest charter school proponents, which financially supported several groups tied to current Secretary of Education Nancy DeVos.
Jeff Hauser, the executive director of the Revolving Door Project, spoke with progressive news organisation The Young Turks, explaining the ire toward Mr Reed from the left.
“Centrist Democrats urging progressives to be ‘team players’ would have better standing to do so if they actually rejected [President] Trump, [Senate Majority Leader Mitch] McConnell, and the rest of the corrupt leaders of the modern GOP. What part of working with Betsy DeVos is being a ‘team player’ on behalf of any progressive goal?” he said.
Mr Reed has been an outspoken advocate for charter schools for decades, including during his time working in the Clinton administration.
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