For House Republicans from Pennsylvania, that means some funding for their own state is at stake.
"The inclusiveness is justified on the merits, and certainly can't hurt to bring additional votes there for the entire package," said U.S. Rep. Chris Smith (R., N.J.), one of the lawmakers pushing for full Sandy funding.
New Jersey and New York officials are counting on some House Republicans' votes to help get the full aid package approved.
In the Senate, Pat Toomey (R., Pa.) joined other fiscal conservatives in voting against the initial $60 billion relief bill, saying it was bloated with spending unrelated to Sandy.
But Toomey isn't opposed to helping his own state. In October he joined Sen. Bob Casey (D., Pa.) in writing to Obama seeking federal aid to help pay for Pennsylvania's preparations for Sandy. He could have a second vote on Sandy relief this month if the measure clears the House.
Toomey, in a statement, said "the federal government must do everything necessary to help" victims of the storm, "and I hope that can be accomplished in a fiscally responsible manner."
Casey, who voted for the Senate package, said Friday, "I'm pleased the administration has done the right thing."
While Pennsylvania escaped the worst of Sandy's impact, the state spent time and money preparing, officials said.
"State and local governments undertook significant protective measures, which, while necessary, strained already overburdened state and local resources," Gov. Corbett said Friday in a statement praising the disaster declaration.
He had urged the state's congressional delegation to push for federal aid.
It was not immediately clear how much money would come to Pennsylvania as a result of the declaration. State estimates put costs of the storm around $22 million, above the $16 million threshold for receiving federal aid.
The effects west of the Delaware River were mostly felt in toppled trees and power outages that affected 1.2 million people.
Thursday's disaster declaration was limited to reimbursements to state and local governments for debris removal, storm preparation, and damage to public properties as well as projects that might mitigate the effects of future storms.
Sixteen counties qualified for aid under Thursday's declaration; only one, Bucks, is in the Philadelphia area.
It is unlikely that Pennsylvania or its counties will meet cost thresholds to qualify for residents to receive aid, said Bucks County's emergency management coordinator, Scott Forster.
U.S. Rep. Mike Fitzpatrick, a Republican who represents Bucks, called Obama's declaration "welcome news" but said he would "continue fighting" to make sure the state receives all the aid "it deserves."
Fitzpatrick and other Republicans from the Philadelphia region could be critical to gathering enough House support for the full Sandy package, facing a vote on Tuesday.
They have been supportive, but next week's vote will cover the more divisive elements in the Sandy aid package.
One vote will be on a smaller version of the relief plan, which has support from House GOP leaders. The second vote is on $33 billion in long-term costs, which faces more opposition from critics concerned about the deficit and wasteful spending.
Support is expected to come mostly from Democrats, but support from two dozen to three dozen Republicans will be needed.
"It's going to be an intense fight," said. U.S. Rep. Robert E. Andrews (D., N.J.).
Pennsylvania Republicans nearly all backed an initial $9.7 billion piece of relief last week, though that portion, for a flood insurance program, was largely uncontroversial.
Contact Jonathan Tamari at email@example.com or follow on Twitter @JonathanTamari. Read his blog "Capitol Inq" at www.philly.com/CapitolInq.