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House Majority Leader Eric Cantor, Virginia Republican, also expressed outrage over the Obama administration’s insistence that contractors not issue the notices about potential layoffs. He said Senate Democrats and Mr. Obama have refused to work with Republicans on ways to avert the defense cuts.

“For an administration that talks a lot about transparency, it is disappointing that they apparently think it is more important to protect their political interests than give hardworking families any indication that they might in fact lose their job in 60 to 90 days due to inaction by the president and Senate Democrats,” he said.

The Jan. 2 sequesters are just the first round. Over the next eight years, another $1.1 trillion in cuts are due, also equally divided between defense and domestic spending.

House Republicans have passed several bills to replace the sequesters with cuts elsewhere, but Senate Democrats have not taken up any of those bills.

Last month, Mr. Obama, acting in accordance with a new law, released a report showing what programs would be cut on Jan. 2.

Among the biggest hits were $21.5 billion directly from operations and maintenance for the Army, Navy, Air Force and Marines and the reserves and National Guard. Tens of billions more would come from procurement and other Pentagon accounts.

Even as Congress and Mr. Obama spar over the round of sequesters, some taxpayer watchdogs are focused on the broader picture — trillions of dollars in debt that will pile up over the next decade unless Washington raises taxes or cuts more spending.

On Monday, Taxpayers for Common Sense released a report proposing $2 trillion in savings over 10 years, nearly half from cuts in special tax breaks.

The biggest cut would be to trim the federal tax deduction allowed for mortgage interest by a third, which could save $645 billion over the next decade. But the group also took aim at Pentagon spending, calling for the Defense Department to cancel an expensive fighter-jet upgrade to the F-35 and stick with the F/A-18E/F Super Hornet, for a savings of nearly $62 billion over 10 years.