The cuts, which will be split evenly between domestic and defense spending programs, are now set to go into effect as of 2013.
Already, some in Congress are suggesting that those cuts might be undone - particularly the military reductions, which Defense Secretary Leon Panetta has suggested could cause men and women in the military undue harm.
In a joint statement on Monday, Republican Sens. John McCain and Lindsey Graham, who both serve on the Senate Armed Services Committee, targeted the defense cuts as "draconian," and said they "cannot be allowed to occur."CBSNews.com special report: America's debt battle
"As every military and civilian defense official has stated, these cuts represent a threat to the national security interests of the United States, and cannot be allowed to occur," the two said in a joint statement. "We are now working on a plan to minimize the impact of the sequester on the Department of Defense and to ensure that any cuts do not leave us with a hollow military. The first responsibility of any government is to provide for the common defense; we will pursue all options to make certain that we continue to fulfill that solemn commitment."
And Rep. Buck McKeon, R-Calif., chairman of the House Armed Services committee, said he would soon be proposing legislation aimed at preventing the trigger cuts, which he argued would do "catastrophic damage to our men and women in uniform."
Leading Democrats have so far signaled that they will not support a change in the sequester rules, however, and Mr. Obama warned Congress Monday he would veto any effort to undo the cuts.
"Already some in Congress are trying to undo these automatic spending cuts," Mr. Obama said, speaking for about four minutes in a live broadcast Monday evening. "My message to them is simple: No."
"I will veto any effort to get rid of those automatic spending cuts," he added. "There will be no easy off ramps on this one. We need to keep the pressure up to compromise, not turn off the pressure. The only way these spending cuts will not take place is if Congress gets back to work and agrees on a plan to reduce the deficit by at least $1.2 trillion dollars. That's exactly what they need to do."
Sen. Minority Leader Harry Reid argued "the sequester was designed to be painful, and it is."
"Make no mistake: we will achieve the more than $2 trillion in deficit reduction we agreed to in August," Reid said in a statement. "The sequester was designed to be painful, and it is. But that is the commitment to fiscal responsibility that both parties made to the American people. In the absence of a balanced plan that would reduce the deficit by at least as much, I will oppose any efforts to change or roll back the sequester.
Panetta said Monday that the defense cuts, if enacted, would be "devastating," and would "tear a seam in the nation's defense."
"The half-trillion in additional cuts demanded by sequester would lead to a hollow force incapable of sustaining the missions it is assigned," Panetta said in a Monday statement. "If implemented, sequester would also jeopardize our ability to provide our troops and their families with the benefits and the support they have been promised. Our troops deserve better, and our nation demands better."
Still, he sided with Mr. Obama that "Congress cannot simply turn off the sequester mechanism."
"Despite the danger posed by sequestration, I join the President in his call for Congress to avoid an easy way out of this crisis," Panetta said. "Congress cannot simply turn off the sequester mechanism, but instead must pass deficit reduction at least equal to the $1.2 trillion it was charged to pass under the Budget Control Act."
Unlike the president, however, Sen. Mitch McConnell put the onus on Mr. Obama, not Congress, to "ensure that the defense cuts he insisted upon do not undermine national security."
"For those of us who hoped that this committee could make some of the tough decisions President Obama continues to avoid, the Democrats' rejection of not one but two good-faith Republican proposals is deeply disappointing," McConnell said Monday. "The good news is that even without an agreement, $1.2 trillion will still be cut from the deficit. Now it falls on the President to ensure that the defense cuts he insisted upon do not undermine national security, as Defense Secretary Leon Panetta has warned."