Congressman Jim Clyburn of South Carolina, the third-ranking Democrat in the House, derided Republicans and the White House for suggesting a short-term extension of enhanced unemployment benefits, saying Sunday that Congress needs to "quit jerking low-income people around."

"This one week, two weeks, this jerking people around is not the way we ought to be conducting ourselves as custodians of this great democracy of ours," Clyburn, the House majority whip, said in an interview with "Face the Nation."

Democratic leaders have spent the last few days meeting on Capitol Hill with White House chief of staff Mark Meadows and Treasury Secretary Steven Mnuchin for discussions on the next coronavirus relief bill. But a deal remains out of reach, as there are several areas of disagreement between the two sides. Chief among them is the extension of $600 per week supplemental unemployment benefits, which expired for roughly 30 million jobless Americans at the end of July.

While Republicans and the White House have suggested a short-term extension of the enhanced benefits, which would give lawmakers more time to negotiate a broader package, Democrats have rejected taking a piecemeal approach.

Clyburn said an unanswered question is what "short term" looks like, whether it's a one-week extension, or six months or 90 days.

"I really think we ought to quit jerking low-income people around," he said. "Let's lay out some security in their lives, some stability in their lives."

Clyburn chided Republicans for not engaging in "any earnest negotiations" and questioned what their red lines are. A proposal unveiled by Senate Republicans last week, which was billed by Democrats as a nonstarter, included funding for a new FBI building and tax relief for businesses, and Clyburn wondered whether those provisions remain on the table.

"I don't know if they're taking the FBI building off the table. They had that in here. Did it take their business 100% deduction for business lunches off the table? I don't know if they have done that. Have they put state or local support on the table? I don't know," he said. "So it's a little bit difficult for me to say what is or is not what I would call earnest discussions, because I don't know where those things are."

The South Carolina congressman said Democrats are "trying to keep ordinary people in focus, people who we depended on as so-called essential workers, the people seem not to think about, at least the Republicans."

While Republicans and Democrats disagree on the additional relief to Americans who have lost their jobs due to the coronavirus pandemic, there is consensus on the need to provide federal aid to schools as they prepare for the start of the upcoming academic year.

But there remains a divide on how much to allocate for education and whether schools should start the year with in-person or online instruction, though a growing number of school districts are adopting a virtual model.

When asked whether he would return to the classroom to teach in the fall, Clyburn, a former public school teacher, said "absolutely not."

"Not until we have a national plan that the school district here in South Carolina ought to be coordinated," he said. "We can't have children going to school when we have not laid out a plan for there to be social distancing, for there to be everybody required a mask."

© 2020 CBS Interactive Inc. All Rights Reserved.