"The only choice I can make would be to hurt fewer poor children and help more special-needs kids, or do the opposite," Duncan said. "It's a no-win proposition."
He said the first to feel the pinch would be school districts in and around military bases and American Indian reservations, entities that receive direct federal aid to make up for lower local property taxes.
Duncan's remarks came a day after the Department of Homeland Security announced that the forced cuts had prompted the immigration enforcement agency to start releasing illegal immigrants being held in immigrant jails across the country.
Carney on Wednesday said the decision was made by career immigration and customs enforcement officials, without input from the White House.
New York Mayor Michael Bloomberg, at the White House to discuss legislation aimed at curtailing gun violence, said the automatic cuts are the equivalent of a "meat ax" and not carefully considered reductions in spending. However, he scoffed at the dark scenarios that have been predicted.
"There's a lot of posturing: 'I'm going to lay off my employees today unless you do something'; 'we're going to close the hospitals down'; 'we're going to take all the prisoners from jail and put them on the street,'" he said, mocking the claims. "Spare me. I live in that world. I mean, c'mon, let's get serious here."
No serious talks to avert the cuts have been under way, and Friday's meeting will be the first face-to-face discussion between Obama and Republican leaders this year.
Republicans were considering offering a measure that would give Obama authority to propose a rewrite to the 2013 budget to redistribute the cuts. Obama would be unable to cut defense by more than the $43 billion reduction that the Pentagon currently faces, and he also would be unable to raise taxes to undo the cuts. The GOP plan would allow the Obama proposal to go into effect unless Congress passed a resolution to overturn them.
The idea is that money could be transferred from lower-priority accounts to accounts funding air traffic control or meat inspection. However, the White House said such moves would offer only slight relief. At the same time, though, it could take pressure off Congress to address the sequester.
In the House, where Republicans in the last Congress passed legislation to replace the cuts, Boehner has said it's now up to Obama and the Senate to figure a way out. The Senate never took up the House-passed bills, which expired when the new Congress was seated in January.