House conservatives say they won’t necessarily insist on offsetting any additional disaster aid following the devastation caused by Sandy, in contrast to their push last year to trade disaster relief for new spending cuts.

Rep. Steve King, R-Iowa, said although he would look for offsets, “I don’t know that that’s a deal breaker at a time like this.”

Pressure is growing on the White House and Congress to beef up funding for the Federal Emergency Management Agency and other federal departments to repair damage that Sandy, which hit the Northeast region as a hurricane and turned into a “superstorm,” spread across several states.

Many Republican lawmakers argue it is fiscally responsible to trim spending in other areas when more money has to be appropriated for disasters. But after a decisive Democratic win in the election, there appears to be little appetite for a battle over offsets.

One freshman conservative, Rep. Tim Huelskamp, R-Kan., said Wednesday he’d like to “wait and see what those numbers are” in a disaster relief request before deciding on whether to call for offsets. “Certainly, this is an interesting and difficult situation we find ourselves in.”

House Majority Leader Eric Cantor of Virginia led a push among Republicans to offset disaster relief last year, but he ultimately dropped his insistence on offsets. Congress passed a stopgap funding measure in October 2011 that provided an additional $2.65 billion in disaster funds without offsets in fiscal 2012.

Cantor spokesman Doug Heye gave no indication Wednesday that Cantor is pushing for offsets this year.

“One of the reasons House Republicans insisted on reforming the disaster funding process, which we did as part of the Budget Control Act, was so that we would have a separate dedicated pot of money available based on historical disaster needs,” Heye said. “We also provided that should a disaster exceed that capacity, Congress and the president could provide additional emergency funds.”

King intends to ask governors whose states were devastated by the storm to submit plans to Congress on where resources would be distributed and how federal funds would be protected from mismanagement.

Since President Barack Obama has not yet asked Congress for additional disaster funds, it is too early to know exactly how lawmakers will react.

Sen. Mary L. Landrieu, chairman of the Appropriations Subcommittee on Homeland Security, warned Republicans not to push for an offset. “They have been very quiet, and that’s very wise of them to be quiet because the public is not on their side,” she said. “Since they just lost this election, they might want to come out on something that would be popular and responsible.”

FEMA is down to about $6 billion in its Disaster Relief Fund, and odds are growing that the agency and other relief programs will need additional funding for storm damage.

More than a dozen senators in states hit by the storm — led by Frank R. Lautenberg, D-N.J., and Charles E. Schumer, D-N.Y. — sent a letter to Obama this week asking him to request additional disaster funds from Congress. But they did not specify how much they believe would be needed.

Landrieu said there is a need for a “robust” supplemental spending bill that would provide more funding than the additional $5.4 billion that Congress can appropriate without breaching the $11.8 disaster funding cap in the August 2011 debt limit law. “I don’t have any idea what the number will be,” she said. “The facts on the ground will dictate that.”

Congress included $6.4 billion for disaster relief in the six-month stopgap funding measure that keeps the government running through March 27. With an $11.8 billion cap on disaster funds, Congress could provide another $5.4 billion either through a supplementary spending bill or as part of a catch-all omnibus spending measure. If more money is necessary, as many expect to be the case, the debt limit law allows Congress to appropriate additional funds under an emergency designation.

Sen. Mike Johanns, R-Neb., said it could be that storm aid is folded into legislation that would avert the fiscal cliff and serve as a “bridge” to agreement on a comprehensive deficit reduction package next year.

“We’re starting to run out of time” to pass a standalone disaster relief bill, he said.

Geof Koss and Ben Weyl contributed to this story.