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The CBO also warned that some of the cuts Congress is counting are from programs where CBO never expected the money to be spent anyway — such as cuts to the Consumer Operated and Oriented Plan, which was part of Mr. Obama’s health care law.

All told, the bill deepens the deficit by nearly $4 trillion over the next decade, when the new tax cuts and spending are combined.

The bill also delays by two months the automatic spending cuts slated to take effect Wednesday, with a promise to reduce spending in the future to cover for part of them.

The deal extends Bush-era tax rates for individuals making $400,000 or less, and for households with incomes of $450,000 or less. It also extends many of the tax credits from Mr. Obama’s 2009 stimulus law, and provides continued enhanced unemployment benefits for those who have been out of work for months.

Mr. Obama gave in on some demands, including accepting a higher threshold for estate and income tax hikes. And the bill also repeals the Community Living Assistance Services and Supports (CLASS) Act, a long-term care program which was part of his 2010 health care law.

The administration had put a hold on the CLASS program but had earlier resisted GOP efforts to repeal it.

David Sherfinski and Tom Howell Jr. contributed to this article.