The requirement on the $60.4 billion measure, which came as the result of a Republican procedural move, could open the door to future requirements to "pay for" disaster assistance with spending cuts. Congress in the past has simply funded disaster aid without such offsets.
The Senate advanced the Sandy aid bill by voting to end general debate and start considering some 21 amendments, many from Republicans aimed at chopping out specific spending requests - including one that would shrink the whole package down to $23.8 billion.
Votes on the amendments and on final passage of the legislation are expected next week after the Senate returns from the Christmas holiday.
The Senate on Friday failed to muster the 60 votes needed to defeat a budget point of order maneuver raised by Republican Senator Pat Toomey. This required that $3.4 billion worth of "mitigation" projects to prevent damage from future storms be included under a cap on discretionary federal spending.
"This will mean real consequences this year," said Democratic senator Barbara Mikulski, the new chairman of the Senate Appropriations Committee. "This is a $3.4 billion unspecified cut that will go to domestic programs for fiscal 2013."
Mikulski, of Maryland, said the cuts would have to be included in spending bills next year that replace a stopgap government funding measure on March 27.
Arguing to defeat the requirement, Senator Charles Schumer of New York, which suffered massively from Sandy's storm surge, said that the move would mark the first requirement for offsetting disaster funds with cuts elsewhere, setting the stage for more congressional fights over it.
"That will mean that disaster money will be much less readily available in the future. The precedent is an awful one," Schumer said.
Toomey, a conservative from Pennsylvania, argued that the $3.4 billion worth of mitigation projects were not disaster aid but simply infrastructure improvement projects.
"That kind of infrastructure spending is the kind of spending that we do routinely, but we plan for it and we budget it," he said. "If it is indeed the priority that many people, including myself, believe that it is, then it ought to be weighed in competition with the other pressing needs."
A senate Republican said the projects targeted in the point of order were not those tied to immediate repairs or reconstruction work, but those that were considered "stand-alone" mitigation projects.
(Reporting By David Lawder; Editing by Nick Zieminski)