Democratic Representative Ocasio-Cortez said on Friday during a House hearing that Mr McConnell, the Senate Majority Leader, was “abandoning our people”.
"Just a day or two ago, the Senate majority leader, Senator McConnell, decided to break the Senate," Ms Ocasio-Cortez said.
"And he broke the Senate as there are thousands of people in Texas lined up for food lines. He broke the Senate while hospitals no longer have beds to house the sick. He broke the Senate, and dismissed the Senate, while 30 million Americans are on the brink of eviction.
“And in breaking the Senate, we are abandoning our people.”
Democratic and Republican lawmakers have so far failed to agree terms on further legislative relief aimed at helping Americans struggling through the pandemic.
Democrats have proposed a package worth $2.2 trillion (£1.7 trillion) while Republicans have pushed a much smaller package of $500bn, bids which each side have rejected.
Ms Ocasio-Cortez added: "He dismissed the Senate when every single day, when we go back to our communities, people are asking us, ‘Where is there going to be help? Is there going to be a second stimulus check? Are we going to get the resources that we need?’
"The Senate prides itself as one of the most deliberative bodies. They abandoned them."
The initial Cares Act passed in March provided Americans with a one-off $1,200 sum and boosted unemployment benefits by $600 a week.
The funding saved approximately 18 million Americans from falling into poverty in April, a study by Columbia University said, but that number fell to only 4 million as of September.
Ms Ocasio-Cortez accused Mr McConnell of having displayed "unconscionable leadership" by allowing senators to take a break for Thanksgiving, warning that “people are going hungry".
"While we are arguing about negotiations and while we are arguing about points, people are going hungry," she said.
"We are dismissing their needs as ‘blue state needs’, or as bailouts depending on what party you voted for. Hungry has no party. Illness has no party."
Before the 3 November election, Speaker Nancy Pelosi and Treasury Secretary Steven Mnuchin tried but failed to agree on a relief package and it is not yet clear if negotiations have resumed.
Coronavirus infections continue to rise across the US, with the country now averaging over 1,300 Covid-19 deaths per day, the highest daily average since May.
The US has recorded more than 12 million cases of the virus since the outbreak gripped the country in March, leading to the deaths of more than 250,000 people, the highest death toll in the world.