The cuts amount to roughly 9% for a broad range of non-defense programs and 13% for the Pentagon over the rest of the current fiscal year, which ends on September 30.
They were included in a 2011 deal to raise the federal borrowing limit as an unacceptable outcome if Congress failed to agree on a comprehensive deficit reduction plan.
However, election-year politics stymied progress on such a deal, leading to the situation Friday in which both sides acknowledged being unable to prevent something neither wanted.
"There are smarter ways to cut spending," said House Speaker John Boehner, R-Ohio, after the meeting with Obama.
Boehner repeated his past assertion that the GOP-led House has offered proposals to replace the forced spending cuts while the Democratic-led Senate has not, as well as his party's opposition to any increased tax revenue to offset the forced spending cuts.
Others who also took part in the White House gathering were Senate Majority Leader Harry Reid, Senate Minority Leader Mitch McConnell and House Minority Leader Nancy Pelosi.
In the White House briefing room, Obama told reporters that Republicans in Congress "allowed these cuts to happen because they refuse to budge on closing a single wasteful (tax) loophole to help reduce the deficit."
"As recently as yesterday, they decided to protect special interest tax breaks for the well off and the well connected and they think that that's apparently more important than protecting our military or middle class families from the pain of these cuts," Obama said.
He was referring to a procedural vote on Thursday in which Senate Republicans blocked a Democratic proposal that called for eliminating some tax loopholes as part of a package with spending cuts.
Boehner and Republicans say the president and Democrats have yet to propose a serious plan to reduce spending, including costly entitlement programs, on a scale necessary to bring chronic federal deficits and debt under control.