Sen. John McCain (R-AZ) talks with reporters at the Capitol. (Chip Somodevilla/Getty Images)

No sooner had the bipartisan supercommittee announced on Monday that it had failed to reach a deal than members had already embarked on round two of the debt fight – the battle over hundreds of billions of dollars in defense cuts set to take effect in early 2013.

In statements issued immediately after the announcement, lawmakers from both sides of the aisle vowed to work to undo the defense cuts that are part of a $1.2 trillion across-the-board cut mandated by the August debt-ceiling deal. Half of the cut, or “sequester,” will affect the Pentagon, while the other half will hit domestic programs.

But some leaders, notably Senate Majority Leader Harry Reid (D-Nev.) took the opposite stance. He argued that Congress designed the “sequester” to be painful and warned that efforts to undo it could have catastrophic effects.

And President Obama left no question about where he stood: in a statement at the White House briefing room Monday night, he threatened to veto any effort by Congress to undo the Pentagon cuts.

“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,” Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.) said in a statement. “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.”

Sen. Carl Levin (D-Mich.), the chairman of the Senate Armed Services Committee, also said that it is now up to Congress to undo the Pentagon cuts and replace them with a deal that both reduces spending and increases taxes.

“The idea of sequestration was to increase the pressure on all sides to compromise,” Levin said. “We must now deal with the sequester as a whole, by doing what the Joint Select Committee has been unable to do: Create a balanced deficit reduction package that includes revenue as well as spending reductions and avoids unacceptable cuts to education, health care, defense and other vital programs.”

Reid left himself some wiggle room on Monday; in a statement, he maintained that he would oppose efforts to re-work the across-the-board cuts “in the absence of a balanced plan that would reduce the deficit by at least as much.”

“Make no mistake: we will achieve the more than $2 trillion in deficit reduction we agreed to in August,” Reid said. “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 House, Armed Services Chairman Buck McKeon (R-Calif.), a staunch opponent of the Pentagon cuts, said that he would introduce legislation “in the coming days” to prevent the spending reductions from taking effect next year.

“Our military has already contributed nearly half a trillion to deficit reduction,” McKeon said. “Those who have given us so much, have nothing more to give. [Defense Secretary Leon Panetta] has said he doesn’t want to be the Secretary who hollows out defense. Likewise, I will not be the armed services chairman who presides over crippling our military. I will not let these sequestration cuts stand.”

House Speaker John Boehner (R-Ohio), who has previously said that he would feel morally “bound” to accept the Pentagon cuts as a result of the supercommittee’s failure, did not directly address the issue in a statement Monday night.

But he seemed to suggest that he would not seek to re-work the cuts – a position that would put him at odds with many members of his own party.

“While I am disappointed, the House will forge ahead with the commitments we have made to reducing government spending and removing barriers standing in the way of private-sector job creation,” he said in his statement.

Some members did not single out the defense cuts in particular but argued that Congress as a whole should still seize the next 13 months to try to succeed where the supercommittee failed.

“This is not the end of the discussion,” Sen. Mark Begich (D-Alaska) said in a statement. “The automatic cuts Congress called for in case the Super Committee couldn’t reach agreement don’t go into effect until January of 2013 which gives us time. As I’ve said all along, we need the right mix of cuts, tax reform and smart investments to get the economy going and reduce the national deficit.”

Other members, including Sens. Mark Kirk (R-Ill.), Joe Manchin (D-W.Va.) and Mark Udall (D-Colo.), called on Monday for Congress to hold a vote on the bipartisan debt-reduction plan produced last year by the Simpson-Bowles commission. Leaders did not immediately respond to their requests.