"This is not a win for anybody," Obama told reporters after the hourlong meeting in remarks reported by ABC News. "This is a loss for the American people."
Obama said the automatic federal spending cuts will go into effect and stressed that, even though they wouldn't be "an apocalypse," the country would pay.
"Not everyone will feel the pain of these cuts right away. The pain, though, will be real," Obama said. "I don't anticipate a huge financial crisis [such as reaching the debt ceiling], but people are going to be hurt."
The sequester crisis, he said, is "just dumb. And it's going to hurt individuals ... and hurt the economy overall."
In a statement shortly after the meeting, House Speaker John Boehner, R-Ohio, said Republicans would maintain their opposition to Democratic proposals that would raise new revenues to offset the cuts.
"The discussion about revenue, in my opinion, is over," he said. "It's about taking on the spending problem here in Washington."
He said the House would take up a bill next week to fund the government past March 27, when the current continuing resolution expires.
"I'm hopeful that we won't have to deal with the threat of a government shutdown while we're dealing with the sequester at the same time," Boehner said. "The House will act next week, and I hope the Senate will follow soon."
Obama earlier declined to answer a question about whether he'd sign a continuing resolution that funded government at sequester levels, saying he would agree to funding levels that were in the Budget Control Act that included provisions for the sequester.
"I think it's fair to say I made a deal for a certain budget [with] certain numbers," Obama said. "I have no problem with that. If the bill that arrives on my desk is reflective of [that] commitment previously made, I'd sign it."
Joining Boehner at the White House meeting were Senate Minority Leader Mitch McConnell, R-Ky.; House Minority Leader Nancy Pelosi, D-Calif.; and Senate Majority Leader Harry Reid, D-Nev. The White House said Vice President Joe Biden also attended.
Obama said he would still push for a sequester replacement.
"My hope is that, after some reflection, as members of Congress start hearing from constituents who are being negatively impacted, as we start seeing the impact that the sequester's having, that they step back and say, all right, is there a way for us to move forward on a package of entitlement reforms, tax reform, not raising tax rates, identifying programs that don't work, coming up with a plan that's comprehensive and that makes sense?" Obama said. "And it may take a couple of weeks, it may take a couple of months, but I'm just going to keep pushing on it."
He said entitlement reform -- noting he risked the displeasure of his own party -- was on the table "if it's part of a broader package of sensible deficit reduction" that includes closing loopholes and eliminating tax breaks available only to wealthy taxpayers.
To those who said his administration was using scare tactics about the effects of the sequester, Obama said, "I guess it depends on where you sit. Not everybody's going to feel it or feel it all at once."
"What is true is the accumulation of all those stories ... is going to make our economy weaker," he said "It's going to mean less growth. The loss of hundreds of thousands of jobs. That's not a scare tactic; that's a fact."
He said he couldn't force Congress -- which broke for the weekend Thursday -- to act on the sequester.
"I am not a dictator; I am the president. ... What I can do is make [the] best possible case about why we need to do the right thing," Obama said. "I can offer concessions. I can offer compromise. I can negotiate. I can make sure my party is willing to compromise. And I think I've done that. What I can't do is force Congress to do the right thing. The American people may have capacity to do that."
The cuts -- which will run through the end of the 2012 fiscal year in September unless lawmakers intervene -- are the first of a decade-long plan to cut spending $1.2 trillion from nearly every federal program, except for military personnel and entitlement programs.