The Senate might pass as early as this week a $60.4 billion Superstorm Sandy recovery package, but it’s far from clear when and how House Republicans will respond to the emergency spending request.

With some GOP lawmakers calling for a smaller measure or spending offsets, House leaders have not settled on a strategy should the Senate send over the Sandy bill, which Democrats want to clear this month.

The Senate Democrats’ wide-ranging disaster package is built on a previously passed House spending bill (HR 1). That means House Republican leaders could seek a conference to try to create a compromise measure out of a Senate-passed bill, allowing for negotiations on many contentious items, including about $13 billion to be provided for long-term work intended to better prepare communities in the Northeast for future catastrophes.

The big question awaiting a final decision is whether to put a conference report for a Sandy supplemental on the floor by itself or wrap it into a larger measure that would also address the fiscal cliff, said Scott Lilly, a former Democratic staff director of the House Appropriations Committee. Speaker John A. Boehner, R-Ohio, may prefer to move a combination package, as he would only need to whip his caucus once on a tough vote in the weeks ahead.

“It just seems to me that Boehner isn’t going to want to use up chits to pass a supplemental” by itself, said Lilly, a senior fellow at the Center for American Progress.

Senate Democrats appear confident they can find the needed seven GOP votes to move the measure this week. Majority Leader Harry Reid, D-Nev., moved Dec. 13 to begin consideration of the measure, with work on the measure to start Monday. Reid could allow senators to freely offer amendments, or seek to block them through a procedure known as filling the tree. Reid may seek a cloture vote to bring consideration of the bill to an end, which requires 60 votes.

Many Republicans have expressed reservations about the scope of the Sandy bill, which would add $11.5 billion to the Federal Emergency Management Agency’s Disaster Relief Fund, the program used to help in the immediate aftermath of catastrophes, and line up funding for transportation and reconstruction projects.

Although criticism of the bill has been muted, several Republicans say they want to see spending cut in other areas to make up for some of the new expenses related to Sandy. The Senate bill does not include such offsets.

“I am going to be open-minded,” Johnny Isakson of Georgia, a conservative Republican, said last week. “They have had a difficult time in New Jersey, and a difficult time in New York, but we have a disaster of a budget process right now, which is exacerbated by the fact that we have only got about $5 billion left in the fund for disasters.”

While waiting for the Senate to act, Democrats and Republicans in the House are pushing for Congress to consider using the tax code to provide some relief to people who suffered losses due to Sandy, mirroring a similar effort already announced by two members of the Senate Finance Committee, Charles E. Schumer of New York and Robert Menendez of New Jersey.

Among the House Republicans backing this effort led by Bill Pascrell Jr., D-N.J., is Michael G. Grimm, a GOP freshman who represents hard-hit Staten Island. Grimm already has been seeking support among fellow Republicans for a Sandy disaster aid package, reaching out in particular to lawmakers from states prone to being hit by hurricanes.

He also has asked House Republican leadership to allow the Sandy recovery package on the floor for a vote without opening it to amendments. That’s likely to be the procedure if the Senate passes a bill, and then GOP leaders seek to go to conference, as conference reports are considered under expedited procedures, with the package then moving as a stand-alone measure. House leaders also could bring the Sandy package on the floor under a closed rule as part of a larger package.

Niels Lesniewski contributed to this report.