He described the situation as "kind of a perfect storm of fiscal problem for us."
The forced spending cuts were part of a 2011 law that increased the nation's borrowing limit. They were intended to be a fiscal cudgel to inspire legislators to compromise on a comprehensive plan to reduce the nation's chronic federal deficits and debt.
However, election-year politics prevented such a compromise, leading to the so-called fiscal cliff at the end of 2012 that resulted in an agreement to stave off pending tax increases for most Americans while allowing rates on top income earners to return to higher levels of the 1990s.
The forced spending cuts set to take effect on January 1 were put off until March 1, and the continuing rift over taxes and spending between Democrats and Republicans prevented a deal to avoid their implementation last Friday.
Now, both sides are seeking to gain a political advantage over the recurring impasse.
"This is no way to run a government but until the president gets serious about the serious structural spending problem that we have, we're gonna have to deal with it," House Speaker John Boehner, R-Ohio, said Tuesday.
The Republican-led House is taking up a GOP-proposed continuing resolution this week, Boehner noted, calling on the Democratic-led Senate to act on it quickly to prevent a government shutdown.
Under the proposed continuing resolution unveiled Monday by House Appropriations Committee Chairman Hal Rogers, R-Kentucky, total government spending for the fiscal year would adhere to the figure negotiated by Obama and Congress minus the cuts.
The proposal would allow Pentagon officials to shift funding to protect top priority programs, and also include provisions to maintain FBI and border security spending.
In addition, it includes some political issues, such as prohibiting any spending for transferring terrorism suspects from the Guantanamo Bay, Cuba, detention facility or for renovating a mainland prison to accept such detainees.
The first response from House Democrats signaled opposition, arguing the Republican measure would further codify the sequester cuts in spending for this year.
"They're happy this is happening," said Rep. Joseph Crowley, D-New York. "You know, if you want to take ownership of it, this is a good way of taking ownership of the sequester, in my opinion. My intention is to vote 'no.'"
However, Senate Democratic leader Harry Reid of Nevada and Carney said Tuesday that the funding levels of the House GOP proposal were acceptable.
Reid and Senate Republican leader Mitch McConnell of Kentucky both said they expected Democrats to make some changes to the House GOP plan, but they expressed optimism that Congress would pass a continuing resolution to prevent any kind of government shutdown.
Later, an administration policy statement expressed openness to negotiating with Republicans on the continuing resolution, but made clear the White House will continue fighting to replace the forced cuts with a package of more tax revenue from closed loopholes and alternative spending reductions.
Overall, the two sides remain ideologically opposed on how to reduce the nation's chronic federal deficits and debt.
Republicans seek to shrink the size of government to lower costs, while Democrats argue some new tax revenue is necessary to maintain the social safety net that protects the elderly, disabled and impoverished.
Polls show the public is about as politically divided as its leaders. While most Americans support a deficit reduction plan that includes spending cuts and increased revenue, as well as entitlement reforms, there is little agreement on the formula for such a package.
A CBS News poll Monday showed that more Americans blame Republicans in Congress than Obama and Democrats for the failure to avert the forced spending cuts, but the gap between the two has narrowed compared to earlier polls by other organizations.
According to the survey, 38% blame congressional Republicans and 33% blame Obama and congressional Democrats, with 19% blaming both. Despite the narrowing gap, the results showed a continued negative perception of Republicans.
Darrell West, the vice president and director of governance studies at the Brookings Institution, said Republicans "have some good cards to play in this debate." After last year's election campaign, in which the main GOP message was to repeal whatever Obama did, Republicans were now "being more strategic in how they're approaching the budget."
"As opposed to saying no to everything, they are picking and choosing their fights," West told CNN.
To Wendy Schiller, a political science professor at Brown University, Obama's campaign-style efforts in recent weeks to blame Republicans for the forced spending cuts and inspire public outrage over them proved to be ineffective and misplaced.
"When people can't see the damage, they don't worry about the damage," Schiller told CNN, later adding: "Americans did not re-elect President Obama to play the partisan blame game; they re-elected him to run the country, and that is what he should be doing."