Back when Congress was trying to reach an agreement to raise the debt limit, leaders from both parties decided they'd only be able to work together with the threat of across-the-board spending cuts hanging over their heads.

So they passed a bill in 2011 that pledged just such across-the-board cuts starting next year, which would affect social spending and the Pentagon budget if Congress couldn't find a way to work together to find a larger solution to Washington's problems.

And now, after failing to reach that bigger solution, the drastic across-the-board cuts are looming.

Congress is trying to find a way to undo some of the spending cuts on Capitol Hill before they take effect. They call it "sequestration" for shorthand, and the automatic budget cuts would drastically reduce social spending and lead to the smallest U.S. military since 1940.

But which priority should be saved?

The drastic automatic spending cuts that could kick in at the end of this year have launched a new congressional quarrel over national priorities and which budget should be saved - the Pentagon or social services.

The law requires $1.2 trillion in automatic cuts equally divided between defense and domestic programs, over the next decade, with the first $109 billion in savings due to take effect Jan. 2, 2013.

The House Budget committee began marking up a bill Monday that would replace the sequestration cuts with alternative spending reductions. Later this week, the House is expected to vote on the GOP's proposal.

Republicans warn that the cuts would place an unfair burden on troops and military families, who would suffer the brunt of Washington's failure to budget responsibly.

"In our view, we shouldn't be taking more from hardworking Americans to fix Washington's mistakes," Rep. Paul Ryan, the chairman of the House Budget committee, said on Capitol Hill Monday. "Instead, we should be solving the problem with structural reforms to our entitlement programs to make them strong and sustainable."

The vast majority of Democrats agree with most Republicans that Congress must avoid the devastating effects of the sequestration, but assert that the GOP goes about it the wrong way, prioritizing defense spending and protecting tax cuts for the wealthy, while undercutting the country's social safety net and other programs intended to build the middle class.

It's the same ideological disagreement that has characterized the divided 112th Congress. After Republicans released their recommendations last week, Rep. Chris Van Hollen, the ranking Democrat on the House Budget committee, said the plan "makes the wrong choices for America" and Democrats will work this week to "draw a strong contrast between the lopsided Republican plan to protect tax breaks for powerful special interests at the expense of the rest of America." Van Hollen, D-Md., added that the Democratic plan "takes a balanced approach to deficit reduction with shared responsibility and shared prosperity."

Democrats contend that the Republicans' recommended cuts would increase the number of children, senior citizens, and others without health insurance and eliminate the Social Services Block Grant, which supports programs like Meals on Wheels for 1.7 million seniors, and child protective services for at-risk children. With the GOP's proposed cuts, Democrats say 300,000 children would lose free school meals and an additional 300,000 would lose health care coverage.

Republicans say their proposal stops future bailouts, restrains spending on government bureaucracies by slashing federal retirement accounts and targeting duplicative spending. And, it goes after fraud by ensuring individuals are actually eligible for taxpayer benefits like food stamps.

The GOP's proposal would also eliminate an element of the Affordable Care Act by cutting funding from the Prevention Fund.

But Democrats warn that as a result, 326,000 women would not get the breast cancer screenings they are slated to receive in the coming fiscal year and 284,000 women would not get the cervical cancer screenings they are slated to receive in 2013.

Finally, Democrats also believe the Republican proposal would weaken the newly created Consumer Financial Protection Bureau by making it subject to appropriations and eliminating direct spending, thereby violating the discretionary spending caps established by the Budget Control Act.

Today, 31 military service and veterans organizations representing 5.5 million people wrote a letter urging Congress to save America's Armed Forces from the "catastrophic impact that sequestration would have on the defense budget and future national security."

"Sequestration would require massive force reductions of more than 200,000, leaving the smallest ground forces since 1940 and a remaining force more vulnerable to emerging threats," the coalition warned in the letter. "It likely would entail breaking compensation, health care, and other support commitments to generations of service members, families, and survivors who already have spent decades sacrificing their personal interests in service to their country."

Even if the House successfully passes its alternative package - a vote is expected Thursday, the Senate is unlikely to approve an identical version of the cuts, further complicating replacing the sequestration.

Congressional sources say they don't expect the sequestration problem to be resolved until after the November election, during the lame duck session.