The sequester was designed as an unpalatable fallback, meant to take effect only if a congressional super-committee failed to come up with at least $1 trillion in savings from benefit programs.
Many of the nation's governors, who are gathered in Washington for their annual meeting, voiced frustration over the impending cuts, saying Washington's inability to strike a deal had created widespread uncertainty in the economy and hampered economic recovery in their states.
"The president needs to show leadership," said Louisiana Gov. Bobby Jindal, a Republican considered a potential 2016 presidential contender, following a meeting with Obama. "The reality is it can be done. This administration has an insatiable appetite for new revenue."
South Carolina Gov. Nikki Haley, a favorite of her party's conservative wing, pointed her anger at both Democrats and Republicans.
"No one should be playing golf. No one should be taking vacations," Haley said, taking a shot at Obama's recent golf outing and Congress' latest recess. "What they need to do is do what these governors do every day. We stay until we get it done."
Democratic Gov. Dannel Malloy of Connecticut concurred.
"They need to get out of that box that sits under the dome and understand that this has real implications in people's lives," he said. "Work with the president, find a way to get it done — or if you want, just turn it over to us governors, and we'll negotiate."
The governors, emerging from a closed-door meeting with Obama Monday, said the president had assured them the administration is pursuing solutions, but offered no assurances that officials would find a way ahead out ahead of the deadline.
Associated Press writers Ken Thomas, Steve Peoples and Josh Lederman contributed to this report.