The supercommittee has until Nov. 23 to agree on how to reduce the deficit at least $1.2 trillion in the next decade. Any amount less than that would be made up in automatic across-the-board cuts divided evenly between defense and domestic programs.
The panel has been stymied for weeks over taxes. Democrats want to raise revenue by making tax-code changes that would directly add money to government coffers.
Republicans have agreed to increase government revenue, but are demanding large cuts to benefit programs, which they say are bleeding Americans dry.
Both sides have blamed the other for failing to move forward. Last week, White House press secretary Jay Carney said that Obama has told panel members that their finished product must contain sources of new revenue, or taxes, as well as spending cuts.
Hensarling offered no new talking points Sunday, indicating that the two sides remain far from reaching consensus.
"We want more revenue. We just want to raise it by growing the economy," he said.
Likewise, Rep. James Clyburn of South Carolina, a Democratic member of the panel, offered no hint that a real compromise was in the works.
"We've got 10 days to do this, and I really believe that all of the ingredients for a good resolution are there. We just need to build the will," Clyburn said.
At the same time, Clyburn accused Republicans of wanting to cut a billionaire's tax bill by $300,000 while eliminating Medicare for people on a fixed income.
"That is just not fair," he said.
Sen. Pat Toomey (R., Pa.), also on the committee, defended his latest proposal as one that would get the economy moving again. Toomey and other Republicans want to generate at least $250 billion in new revenue by limiting tax deductions but only if Democrats agree to drop the top tax rate from 35 percent to 28 percent.
"You absolutely can do this in a way that will be pro-growth, that will generate more revenue, that would avoid this huge tax increase that's coming otherwise," Toomey said.
Democrats have rejected the idea as something that will ultimately cost more than it would save, and called for a mix of $1 trillion in spending cuts and $1 trillion in higher tax revenue over the next decade.
Sen. Mark Warner (D., Va.), who supports entitlement and tax changes, suggested that politics was the biggest culprit in preventing a deal.
"You'll know this supercommittee is getting close when folks on both ends of the political extreme scream the loudest, because that will show that there's actually movement being made," he said.
Sen. Tom Coburn (R., Okla.) agreed.
"We can fix our problems but we require leadership from the president, and the leaders from the House and the Senate to say 'we're going to do this.' And we have not seen that on both sides of the aisle and that's disappointing," he said.
Coburn, a vocal opponent of any tax increase, said he could stand the idea of increasing government revenue if the money comes from restructuring entitlement programs.
"I want to tell you, we're going to touch Medicare because there's no way we can borrow the money five years from now to run Medicare the way it is today," he said. "The question really is, will politicians do what is best for the country or best for their party and position?"
Hensarling, Warner, and Coburn spoke on CNN's State of the Union. Toomey and Clyburn were on Fox News Sunday.