Washington (CNN) -- Uncertainty lingered Tuesday about what the continued fallout would be from the failure of the congressional "super committee" to forge a deficit reduction deal.
Monday's announcement about the committee's failure was followed by a dip in the Dow Jones Industrial average. The Dow fell 248 points Monday, with a minor recovery after being down more than 300 points earlier in the afternoon.
President Barack Obama and congressional leaders traded blame Monday for the failure and called for Congress to work out an agreement before painful automatic budget cuts take place in 2013.
On Monday, the co-chairs of the bipartisan special joint committee said in a statement that "after months of hard work and intense deliberations, we have come to the conclusion today that it will not be possible to make any bipartisan agreement available to the public before the committee's deadline."
Initial reaction had Democrats and Republicans blaming each other for the inability of the bipartisan committee to negotiate at least $1.2 trillion in deficit reduction measures.
Obama said Republicans in Congress rejected what he called a balanced approach to deficit reduction that included tax increases on the wealthy.
"Despite the broad agreement that exists for such an approach, there are still too many Republicans in Congress that have refused to listen to the voices of reason and compromise that are coming from outside of Washington," Obama told reporters after the committee announced its failure.
Senate Majority Leader Harry Reid, D-Nevada, said Democrats "were prepared to strike a grand bargain that would make painful cuts while asking millionaires to pay their fair share, and we put our willingness on paper," but Republicans "never came close to meeting us halfway."
His GOP counterpart, Sen. Mitch McConnell of Kentucky, argued that an agreement "proved impossible not because Republicans were unwilling to compromise, but because Democrats would not accept any proposal that did not expand the size and scope of government or punish job creators."
Republican presidential contenders complained that Obama had failed to display necessary leadership to forge an agreement, an accusation rejected by White House Press Secretary Jay Carney.
"Congress assigned itself a job; assigned 12 of its own members a task -- a task that wasn't really that difficult to achieve if there was a willingness to compromise," Carney said of the so-called super committee created under the debt ceiling agreement earlier this year. He added, "Congress needs to meet its responsibilities."
Others lamented and criticized the missed opportunity.
"On its current course the federal government is projected to spend almost $44 trillion over the next 10 years, and it is nothing short of an embarrassment, an absolute national disgrace and failure of leadership that we cannot agree on even a paltry $1.2 trillion in deficit reduction over that time frame," Republican Sen. Bob Corker of Tennessee said in a statement.
Meanwhile, independent Sen. Joe Lieberman of Connecticut, who caucuses with the Democratic majority, called for a "bipartisan rebellion" in Congress to strike a deficit deal in the wake of the committee's failure.
Noting that three deficit reduction plans have been proposed, including one by a special commission appointed last year by Obama, Lieberman called for "a vote on the Senate floor before the end of this year and show that elected officials in Washington are capable of protecting the economic future of the American people."
All three of the plans Lieberman referenced came from bipartisan groups, and all called for a comprehensive package of spending cuts, increased tax revenue and reforms to entitlement programs such as Social Security and Medicare.
Obama and Democrats consider such an approach the only balanced and fair way to reduce mounting federal deficits and spread the impact across all sectors of society. Republicans seek to shrink government spending and the overall size of government, and therefore reject virtually any kind of increased tax revenue.
Both Obama and House Speaker John Boehner, who failed to strike a major deficit reduction agreement earlier this year, called for Congress to continue working for an outcome that would best serve the national interest.
"This process did not end in the desired outcome, but it did bring our enormous fiscal challenges into greater focus," said a statement by Boehner, R-Ohio. "I am confident the work done by this committee will play a role in the solution we must eventually find as a nation."
Legally, a majority of the 12-member committee had until midnight Wednesday to reach an agreement, but any deal needed to be announced for legislative reasons by the end of Monday.
Failure by the committee, evenly split between six Democrats and six Republicans from the House and Senate, sets in motion an alternative timetable for $1.2 trillion in spending reductions starting in January 2013.
Leaders on both sides of the aisle are unhappy with the nature of the fallback plan, which cuts evenly from domestic and defense programs. Social Security, Medicaid, food stamps, veterans' benefits and other politically sensitive programs are spared the budget ax.
Pressure has already started to undo a number of cuts included in the fallback plan, which was a product of the summer debt-ceiling agreement. Defense Secretary Leon Panetta and key Republicans argue that the military will be undermined by excessive reductions to the Pentagon budget.
McConnell raised the idea of softening the automatic cuts in his statement, trying to depict it as a responsibility belonging to the president.
"The good news is that even without an agreement, $1.2 trillion will still be cut from the deficit," McConnell's statement said. "Now it falls on the president to ensure that the defense cuts he insisted upon do not undermine national security."
However, Obama made clear that he would veto any attempt to undo or alter the automatic spending cuts, known as a sequester mechanism.
"The only way these spending cuts will not take place is if Congress gets back to work and agrees on a balanced plan to reduce the deficit by at least $1.2 trillion," he told reporters. "That's exactly what they need to do. That's the job they promised to do. And they've still got a year to figure it out."
Obama also sought to reassure markets and ratings agencies that even without an agreement by the special committee, the automatic cuts now scheduled to occur mean significant deficit reduction steps will take place.
"One way or another, we will be trimming the deficit by at least $2.2 trillion over the next 10 years," he said, referring to a previous agreement for cutting $1 trillion in spending and the required $1.2 trillion in further cuts triggered by the committee's failure.
The ratings agency Standard & Poor's issued a statement Monday that said the committee's failure to reach agreement would not bring a downgrade of the U.S. credit rating, as long as the resulting automatic spending cuts remain intact.
At the same time, it remains unclear how the sharply divided Congress will reach agreement on a series of looming budget decisions, including an expiring payroll tax cut and calls for a new extension of unemployment benefits. Both questions need to be dealt with by the end of December.
Democrats have blasted Republicans for not being more receptive to higher taxes on the wealthy, while Republicans insist Democrats are unwilling to make necessary spending cuts to popular domestic programs.
Super committee member Sen. John Kerry, D-Massachusetts, told CNN on Monday that Republicans undermined any prospect for genuine compromise by being unwilling to phase out the Bush-era tax cuts for upper-income Americans.
"We got totally hung up by people who were insisting that not only could they not raise any additional revenue from the wealthiest people in the world, but they wanted to give them an additional tax cut," Kerry said. "This is insanity."
Fellow panel member Sen. Jon Kyl, R-Arizona, said Democrats risked throwing the economy back into a recession by trying to use the super committee's mandate to raise taxes on small businesses and other drivers of job creation.
"Our Democratic friends said we won't cut one dollar more without raising taxes," Kyl said. "That tells you a lot about the ethos in Washington. We went into the exercise to try to reduce federal government spending. What we get from the other side is, no, we won't make more cuts unless you raise taxes."
At the center of the dispute is conservative activist Grover Norquist, head of the group Americans for Tax Reform and author of a popular GOP campaign pledge never to raise taxes.
Democrats portray Norquist as a zealot who has effectively imposed a reign of terror over congressional Republicans petrified of crossing his group and incurring the wrath of the GOP's anti-tax base.
"Grover has been the 13th member of the (super committee) without being there," Kerry said. "I can't tell you how often we hear about the pledge."
CNN's Jessica Yellin, Alan Silverleib, Tom Cohen and Lisa Desjardins contributed to this report.