The stimulus stalemate has left lawmakers at odds over how to get more relief to millions of Americans who need it.
Earlier this month, Senate Republicans attempted to get a smaller bill through Congress as the standoff between both parties continued.
But that relief bill did not include a second round of $1,200 stimulus checks, a measure that both parties had all but signed off on. The bill failed to get the 60 votes it needed to advance.
Still, House Democrats pushed back on the stimulus check exclusion on Tuesday during a congressional hearing with Federal Reserve Chairman Jerome Powell and Treasury Secretary Steven Mnuchin.
"The economic impact payments must be made because the rent must be paid," said Rep. Al Green, D-Texas.
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"If we do not do this, we will put persons at risk of being evicted at a time when we are having a pandemic that is still taking lives in this country," he said.
Green also said a new Government Accountability Office report that found the Treasury Department does not have adequate data on the number of people who qualify for the first stimulus checks, but who have not yet received them, is cause for concern.
The number excluded, including gig workers, could be in the millions, he said. The IRS is in the process of mailing letters to about 9 million Americans to notify them that they may be eligible for the money.
Rep. Rashida Tlaib, D-Mich., also spoke out about the prospect of a second round of payments, asking Mnuchin, "Yes or no, do you believe another stimulus check could help stabilize the economy?"
"I do," Mnuchin said. "The administration does support another stimulus payment."
The likelihood and timing of that money still remains unclear. House Democrats and Senate Republicans had both put forward proposals that included a second round of direct payments. Other issues, however, have made it impossible for both sides to come to an agreement, at least for now.
"We obviously can't pass a bill in the Senate without bipartisan support," Mnuchin said. "Our job is to continue to work with Congress to try to get additional help to the American public."
In response, Tlaib urged Mnuchin to push for more stimulus checks.
"I think you need to be very clear with the senators … that direct payments to individuals is critical to preventing economic collapse in our country," Tlaib said.
Some experts have speculated that the death of Supreme Court Justice Ruth Bader Ginsburg, and the ensuing fight over the nomination to fill the now vacant seat, could make it impossible for Congress to come up with another coronavirus stimulus deal now.
In a separate interview with CNBC on Tuesday, Larry Kudlow, director of the National Economic Council, dismissed that idea as "not necessarily a given." The two parties were already at odds before the judicial issues came up, he said.
The White House is advocating for another package targeting "kids and jobs," Kudlow said. That would include more than $100 billion to help schools and another $100 billion to extend Paycheck Protection Program funds to small businesses.
"I wish we could break the stalemate, because even though I think the economy is improving nicely, I think it could use some help in some key targeted places," Kudlow said.