WASHINGTON — Senators showed broad support Friday for $60.4 billion in emergency funding for victims of Superstorm Sandy, voting overwhelmingly to bring it up for final passage next week.

The motion passed 91-1.

Several Republican senators, concerned about the high price tag, were successful in forcing cost offsets for about $3.5 billion of the overall bill, a move that frustrated Democrats from the affected states because they said the aid should be approved without cutting spending elsewhere.

Supporters hope the momentum they got in the Senate will translate into swift House action next week, although key Republicans in the House have said they want to approve a much smaller bill.

If a final bill is not approved before January 3, when the new 113th Congress convenes, supporters will have to start the entire process over again, something they are trying to avoid.