Northeast lawmakers whose states were damaged by Superstorm Sandy are finally seeing the House action they have been demanding on disaster relief funding.

But the measure expected to win passage on Friday, more than two months after the storm, is only a first installment of the more than $60 billion the White House has requested. Getting the rest of the money through the House and Senate — probably in two more pieces on the House side — will take weeks and could prove difficult.

The $60.4 billion aid package the Senate passed in December died in the House on Thursday when the 112th Congress ended and the 113th was sworn in.

After an uproar that saw Speaker John A. Boehner, R-Ohio, harshly criticized by New York and New Jersey Republicans, leadership placed Sandy relief at the top of the legislative agenda for the new Congress.

The House is set to pass a measure Friday to provide $9.7 billion in additional borrowing authority for the National Flood Insurance Program and avert a delay in payment on about 115,000 claims. The Federal Emergency Management Agency said Wednesday that without additional borrowing, the flood insurance program will run out of money for claims next week.

The bill will be considered in the House under expedited procedures normally reserved for noncontroversial measures. A Democratic leadership aide said the Senate will attempt to clear that measure by unanimous consent on Friday, following House passage.

Flood insurance funding will be the easiest part of the recovery package to move. Conservatives in both chambers may put up a fight when the House turns Jan. 15 to measures intended to provide the remaining $50 billion sought for the recovery by the White House. Conservative groups including Heritage Action and the Club for Growth objected last month to the Senate’s package, which included money for purposes unrelated to Sandy.

House Republicans from New York and New Jersey are working with Democratic colleagues to overcome concerns about the spending level. The increased number of House Democrats in the new Congress could make their task a little easier, but the Northeast Republicans will need to work hard to round up votes in the GOP conference. Republicans representing districts prone to weather-related disasters are probably the most likely to lend their support.

“I don’t think that there is anyone in this House who is going to be able to overcome the New York-New Jersey delegation,” said Rep. Michael G. Grimm, a Republican who represents hard-hit Staten Island, N.Y. “I think that the team will be able to get this done, I really do.”

The House will likely consider the additional $50 billion in Sandy aid in two parts, as Appropriations Chairman Harold Rogers, R-Ky., proposed in the 112th Congress earlier this week. The House would first try to pass a bill likely to provide about $18 billion to address the more immediate recovery needs including money for FEMA’s disaster relief fund. Sandy has caused the fund’s balance to drop to $3.94 billion as of Dec. 31, from more than $7 billion on Oct. 1.

A more controversial third measure would include about $33 billion for longer-term mitigation projects, such as major repairs and rebuilding roads and transit systems to better withstand future storms.

The Senate leadership aide said the majority will wait to see what emerges from the House before deciding how to proceed with Sandy aid beyond the initial flood insurance money.