And House Republicans said they wanted to sharply cut the amount of aid offered to communities devastated by the late-October storm that killed at least 131 people in the United States and caused more than $63 billion in damage.
Rep. Steve King, R-Iowa, a member of the Tea Party caucus, was among conservative House lawmakers saying they wanted offsets for at least part of the spending.
He told The Hill newspaper a great deal of disaster-relief money after 2005's Hurricane Katrina disaster was wasted.
"We saw a lot of money that was spent down in Louisiana that should not have been," he said. "We saw a lot of blank checks that should not have been written.
"I am going to look for offsets as well, but I can see some circumstances where they won't be needed if the proper restraints are in place," King said.
But some GOP senators said disaster aid shouldn't have to be met with dollar-for-dollar offsets.
"Offset where you can, but this is truly an emergency," Sen. Lindsey Graham, R-S.C., the second-most senior member of the disaster-recovery subcommittee, told Politico.
Sen. Dan Coats, R-Ind., the top Republican on the panel overseeing the Federal Emergency Management Agency, separately told Politico, "If you're looking for emergency help that has to get out there right now, in the context of this budget debate going on, I think we have to understand that we might not be able to get viable offsets."
The White House asked Congress a week ago to pass a $60.4 billion bill to pay for damage resulting from Sandy.
The administration designated about $55 billion as immediate emergency disaster aid and almost $13 billion for long-term efforts to mitigate future natural disasters.
Leadership aides in the Democratic-controlled Senate said the upper chamber could take up the funding as early as Friday.
The Senate bill, based on the White House request, includes $200 million to restore and protect coastal ecosystems, $3 million to replace damaged law-enforcement vehicles and $398 million to repair national parks, including the Statue of Liberty and Ellis Island.
But House Appropriations Committee Chairman Hal Rogers, R-Ky., told Politico the GOP-controlled House would likely have no debate on the lower chamber's version of an aid bill until after Christmas.
New York and New Jersey officials have said they don't want to wait for the House debate until next year.
A senior GOP House aide told The Wall Street Journal the emergency-funding bill House lawmakers intend to introduce, in any case, would be "far smaller" than the amount the administration asked for.
That amount is itself $22 billion less than the request from the governors of New York, New Jersey and Connecticut.
Two senior GOP House aides told the Journal the Obama administration didn't provide enough information to justify spending anywhere near $60.4 billion.
The first aide told the Journal it was too early to say how much money the committee would recommend.
Between $5 billion and $6 billion would be immediately available to FEMA under the Budget Control Act signed into law last year, the aide said.
Republican Gov. Chris Christie said Thursday New Jersey's 21 counties could now apply to FEMA for reimbursement of 75 percent of the cost of municipal debris removal from private property.
Counties, cities and towns will have to cover the remaining 25 percent of the cost, Christie said in a statement. The ratio is standard for cost sharing for qualified public-assistance expenses, he said.