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“We can’t just cut our way to prosperity,” he said.

The meeting between his top economic and policy advisers and the leaders of top defense companies was meant to highlight the job consequences of defense cuts.

“For some of these major companies, the impacts would be long-lasting,” Mr. Carney said afterward. “A company like Northrop Grumman would have 20,000 small businesses in their pipeline that would be severely affected.”

The cuts are so bad that both sides of the political aisle are trading blame over who put them into place.

Bob Woodward of The Washington Post wrote in a book last year that the sequesters were the White House’s idea, though congressional Democrats say House Speaker John A. Boehner, Ohio Republican, agreed to them.

Sen. Lindsey Graham, South Carolina Republican, said both sides should shoulder responsibility.

“We bear responsibility as Republicans for allowing this to happen. Lead us to a better solution,” Mr. Graham said.

If Mr. Obama fails, he said, he would “go down in history, in my view, as one of the most irresponsible commanders in chief.”

For now, it’s not clear whether either chamber will take action.

Mr. McKeon said he would like the House to vote on his proposal as soon as possible.

The House schedule next week will be dominated by a bill to halt federal civilian-workforce pay raises, and Congress is scheduled to be out the week after that to commemorate George Washington’s birthday.

Senate Majority Leader Harry Reid, Nevada Democrat, said this week that he would like to bring up a package of tax increases for a vote, but it’s unclear whether it can pass.

Mr. Boehner said the House last year, in the previous Congress, passed bills to avert a sequester and that the next move is up to Senate Democrats.