Updated: 5:53 p.m. ET
After weeks of fraught negotiations and high-stakes bargaining between White House officials and Republican and Democratic leadership, the House began debate on Monday over a.
The deal, which was brokered on Sunday night in last-minute negotiations between the White House and Senate Minority Leader Mitch McConnell, R-Ky., would cut nearly $1 trillion in government spending over the next 10 years and raise the amount of money the U.S. is legally allowed to borrow by enough to potentially avoid another showdown on the matter before next year's presidential election.
It would also create a special congressional committee of a dozen members -- three from each party from the House and the Senate - that would be tasked with coming up with recommendations for $1.5 trillion in further deficit reductions by Thanksgiving. Those reductions could include cuts from defense and social safety net programs, as well as changes to the tax code.
Senate leadership aides told CBS News' John Nolen that the Senate will vote on the debt plan Tuesday at a time yet to be determined.
Vice President Joe Biden said Monday afternoon he was "confident" the legislation will pass - but the bill is sure to, particularly in the House of Representatives, where Tea Party Republicans fought fiercely for a balanced budget amendment, and Democrats pushed for the inclusion of revenue increases.
Biden met with the House Democratic Caucus for an hour and a half on Monday in an apparent attempt to win Democrats over to the deal.
"I went to explain and lay out exactly how we got to [where we are] and why it's so important for the country," Biden told reporters after emerging from the meeting. "My sense is that [House Democrats] expressed all their frustration - which, I'd be frustrated if I were sitting there as well... They asked questions specifically about the proposed legislation."
But, he noted, "I thought it was a good meeting. And I feel confident that this will pass."
Biden conceded that the deal would have been significantly different if "circumstances in the Congress" were different, and that, in that case, "we would be talking and should be talking right now about job creation initiatives" and "investment and innovation."
"But the truth of the matter is...this is the debt limit," he said. "Unless certain compromises were made, we would default on our debt."
The deal appears to be gaining traction among House Republicans, although most Tea Party members are expected to vote against it. If that pattern holds true, the bill's future will largely depend on House Democrats.
When asked if the bill would pass the House, she reportedly responded: "You'll have to ask the speaker. He has the majority."
In an interview with CBS News Capitol Hill Correspondent Nancy Cordes, however, Pelosi said she would support the debt deal herself because it was just about "adequate."
"I don't think it's a bill Democrats would be happy with because it doesn't share our values," Pelosi told Cordes. "However, it must be done. We have to avoid default."
CBS News' Jill Jackson reports that the Congressional Black Caucus members will withhold from voting as a block until Republicans deliver a majority of their members in favor of the package. Many Democrats may also delay their votes until it is clear how many Republicans vote for the plan.
In remarks to reporters on Monday, Pelosi said that while final compromise included "some successes," the bill also had major sticking points.
"They have had some successes in this in terms of protecting beneficiaries of Medicare and Medicaid and Social Security. That's important to us. And having an 18-month, at least, extension that can help us get on with the business of growing the economy and creating jobs - that's important to us," she said.
But, she continued, "on the other side of the grid, we have problems with no revenue in the bill when we are having severe cuts - and we need to make some cuts, but severe cuts and initiatives that impede the education of our children, our clean air, clean water, food safety - you name it - while not one red cent from our wealthiest people in our country. You have to weigh these attributes and that's what we're doing right now."
In remarks at the Capitol on Monday, Sen. Majority Leader Harry Reid, D-Nev., said he was "hopeful" that the plan would be approved - but he emphasized that "I never count my votes until they're cast."
At issue with progressives is the bill's failure to include mandatory revenue increases. And while the White House has expressed its hope that the so-called "super committee" would include revenue hikes, Republican members of the bipartisan group will surely resist those increases.
In his daily press briefing, White House Press Secretary Jay Carney said it was the administration's "expectation" that the second round of deficit reductions would include revenue increases.
Failing that, he said, "you can be sure that the president will honor his promise to veto any legislation that would extend the Bush high-income tax cuts beyond 2012, which would, of course, create nearly $1 trillion in revenue-raisers when that happens."
"In the end, compromise won out," Carney argued.
Not everyone agreed with that assessment.
Rep. Emanuel Cleaver, D-Mo., head of the Congressional Black Caucus, said the plan would put Medicare "on the chopping block" and tweeted Monday morning, "This deal is a sugar-coated satan sandwich. If you lift the bun, you will not like what you see."
"This debt deal is antithetical to everything the great religions of the world teach, which is take care of the poor, aged, vulnerable," he added.
"This is not a balanced approach," said Rep. Steny Hoyer, the No. 2 Democrat in the House, in a Monday interview on CBS' "The Early Show." "Revenues need to be on the table, and we haven't done that."