Obama called on congressional Republicans to compromise and accept the Senate Democrats' proposal.
The Democrats propose to generate revenue by plugging some tax loopholes. Those include tax breaks for the oil and natural gas industry and businesses that have sent jobs overseas, and by taxing millionaires at a rate of at least 30 percent.
A spokesman for House Speaker John Boehner said the Ohio Republican agrees the sequester is a bad way to reduce spending, but put the onus for averting the cuts on Democrats.
"A solution now requires the Senate — controlled by the president's party — to finally pass a plan of their own," spokesman Brendan Buck said.
Meanwhile, a bipartisan proposal Tuesday by co-chairs of an influential deficit-reduction commission called for reducing the deficit by $2.4 trillion over the next 10 years, with much of the savings coming through health care reform, closing tax loopholes, a stingier adjustment of Social Security's cost of living increases and other measures.
The proposal by former Republican Sen. Alan Simpson of Wyoming and Democrat Erskine Bowles, the former chief of staff for President Bill Clinton, calls for about one quarter of the savings to come from changes in health care programs and another quarter from revenue generated by tax changes.
In their plan, Bowles and Simpson say the automatic cuts scheduled for March 1 are too steep and could set back the economy.
"Sharp austerity could have the opposite effect by tempering the still fragile economic recovery. In order to protect the recovery, the sequester should be avoided and deficit reduction should be phased in gradually," they wrote.
Some Republicans, including House Budget Committee Chairman Paul Ryan, R-Wis., have advocated plugging loopholes, but as part of a discussion on a tax overhaul, not sequestration.
"Loopholes are necessary for tax reform," Ryan said Sunday on ABC's "This Week." ''If you take them for spending, you're blocking tax reform and you're really not getting the deficit under control."
The sequester was first set to begin taking effect on Jan. 1. But as part of the "fiscal cliff" negotiations, the White House and lawmakers agreed to push it off for two months in order to create space to work on a larger budget deal.
With little progress on that front in recent weeks, Obama is calling for the sequester to be put off again, though it's unclear whether another delay would have any impact on the prospects for a broader budget agreement.