The law increases the borrowing authority of the Federal Emergency Management Agency. FEMA had warned that it was set to run out of money without additional dollars from Congress.
The White House said more than 100,000 flood claim payments from Sandy would be delayed without the additional money.
The House has yet to act on a larger, more comprehensive Sandy aid package. Republican leaders did not bring the bill to the floor before the last session of Congress adjourned.
House Speaker John Boehner has promised a vote Jan. 15 on that $51 billion package, and Senate leaders have promised a vote the following week.