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But most lawmakers argue that Congress always has covered costs to recover from natural disasters and that this time should be no different.

They also point to emergencies while Republicans were in power, including Hurricane Katrina, which struck New Orleans and Mississippi in 2005. The Republican-controlled Congress and President Bush pumped tens of billions of dollars into recovery and reconstruction without offsetting the cost.

The Congressional Research Service said that of 59 emergency spending bills passed since 1990, only six were fully offset by cuts elsewhere. The agency said that would be difficult in this situation because the request was so large.

Most of the Sandy money won’t be spent until fiscal year 2014, but Northeast lawmakers wanted it budgeted now.

The government is projected to run a deficit of about $1 trillion in fiscal year 2013, which began Oct. 1. Revised estimates are due next week from the Congressional Budget Office.

Mr. Obama campaigned on reducing deficits by allowing tax rates to rise on families making more than $250,000. In the end, he cut a deal that ended the payroll tax holiday, raised rates on families making more than $450,000, and limited exemptions and deductions for those making more than $300,000.

Overall, that deal means far deeper deficits than if Congress allowed all Bush-era tax cuts to expire. But the White House argues that since Republicans in Congress wanted to extend all tax cuts, allowing some to expire means that revenue should count as new savings.