But reaching a deal on the next question -- what exactly to replace the cuts with -- will require yet another round of bitter political fighting on Capitol Hill.
President Barack Obama is launching a new effort to dial back the spending cuts. He's highlighting the issue on Thursday evening when he meets with House Democrats at a retreat in Philadelphia. And the budget blueprint he'll unveil on Monday will call on Congress to do away with the controversial billions of dollars in automatic spending cuts that went into effect in 2013 after lawmakers failed to reach a budget agreement.
Congressional leaders on both sides of the aisle are quick to acknowledge that there are better ways to rein in the deficit than another round of drastic across-the-board cuts to defense and non-defense spending, scheduled to kick in this fall. But any path to a budget compromise will once again expose the deep ideological divide between Democrats and Republicans on how to cut the deficit.
A spokesman for House Speaker John Boehner (R-Ohio) told reporters this week that Republicans have passed legislation on multiple occasions to replace the sequester only to have the president demand tax hikes, making it impossible for Republicans to "take him seriously."
"You'd be very hard pressed to find someone who says this sequestration is great budget policy," said Jared Bernstein, a senior fellow at the Center on Budget and Policy Priorities and a former economic adviser to Vice President Joe Biden. "What's challenging is figuring out how to raise the caps in a way that everybody can agree on."
Obama's budget will propose raising the defense spending cap by $38 billion and the non-defense spending limit by $37 billion, boosting total discretionary spending levels by about 7 percent.
There is widespread concern across the political spectrum that the recent cuts to the defense budget have put the country's national security at risk. That sets the stage for possible infighting among Republicans between defense and fiscal hawks on how exactly to offset higher defense spending. It could be a particularly difficult task given that many in the party adamantly oppose raising taxes.
"While I can see Republicans agreeing to raise the defense cap, it's going to be hard for Republicans to raise the non-defense cap because they also want to get to a balanced budget," said William Hoagland, senior vice president at the Bipartisan Policy Center and a former senior Republican staffer on the Senate Budget Committee. "They can't do those two things without somehow finding a way to offset it."
Complicating matters for the next round of budget negotiations is the brightening economic outlook. The sequester set off alarm bells in 2013, with economists warning that such deep spending cuts could permanently hamper the economic recovery.
Two years later, economic growth has picked up significant steam -- an outcome that could bolster calls to keep the current spending caps in place.
"The president noted during the State of the Union that the deficit is at the lowest level during his presidency. The sequester is a large reason for that," said Nicole Kaeding, budget analyst for the libertarian-leaning Cato Institute. "The sequester has helped, not hurt, the recovery."
It's not just the GOP that may see some internal chafing.
For Democrats, who argue the economy could have made bigger strides were it not for sequestration, one big question is how hard to push for higher non-discretionary spending. Many have made the case that Republicans' insistence on deep spending cuts have choked off funding to programs critical to long-term economic growth, in areas like research, education and infrastructure.
"For too long, the draconian cuts of the sequester have strangled our investments to keep America No. 1 in the global economy and to ensure our national security," House Minority Leader Nancy Pelosi, D-Calif., said Thursday.