'Big Deal': $4T Budget Cut Package on Table, Sources Say

President Obama, Sen. Boehner again talking about debt ceiling deal.

WASHINGTON, July 17, 2011— -- With the country's credit card about to be cancelled, the White House said today there is still time to cobble together a "big deal" to lower the deficit.

President Obama's budget director, Jack Lew, says even though only a few days remain to start the legislative process to raise the debt ceiling, he is confident something will be approved.

"I believe the debt will be extended," he said on ABC's "This Week." "I think notwithstanding the voices of a few who are willing to play with Armageddon, responsible leaders in Washington are not."

And it does appear the "big deal" is back on the table. Capitol Hill sources tell ABC News that Obama and Republican House Speaker John Boehner are again talking about reducing the deficit by more than $4 trillion over the next decade or so. Boehner reportedly wants the president to lay out specific cuts to entitlement programs. But many Republicans doubt such a plan can get through Congress.

Over the weekend the two leaders in the Senate continued to devise a "plan B" to avert the country from potentially defaulting.

"That's what the Senate is proceeding with," Republican Sen. Jon Kyl of Arizona said this morning on ABC's "This Week with Christiane Amanpour." "Now, the House of Representatives has to make its decision about what it will do. But I'm simply answering your question, at the end of the day, I don't think there will be a default."

The plan would give the president the authority to raise the country's debt ceiling, while allowing Congress to avoid having to directly vote for the measure.

"It takes the pressure off all the politicians, but it allows us to pass a debt limit without making the hard choices that this country has to make," Republican Sen. Tom Coburn of Oklahoma said this morning on CBS' "Face the Nation."

The standoff between Republicans and Democrats is led by House Majority Leader Eric Cantor of Virginia and a group of other Republicans on Capitol Hill who refuse to consider tax increases as part of the deal.

While many Republicans refuse to consider tax hikes, some Democrats are unwilling to compromise on entitlement programs. House Democratic Leader Nancy Pelosi says she won't accept a deal that includes cuts to entitlement programs like Social Security and Medicare.

Though many throughout the country are calling for Washington to strike a deal, both Cantor and Pelosi are getting some support from the constituents in their home districts.

While some within Cantor's Virginia district are calling for him to compromise, others say the majority leader should stand his ground.

"They need to hold the country to task, we need to pay our way out of debt," says Virginia resident Hugh Burkhart.

Similarly, Pelosi is receiving support from residents in her California district.

"She should only be willing to compromise if others are willing to come to the table with some compromise too," says California resident Gia Brazil.