The lawmakers will vote on the $9 billion for the national flood insurance program. A second vote will be held Jan. 15 on the remaining $51 billion in the package. The new Congress is being sworn in Thursday.
Since the votes will be taken in the new Congress, the Senate also will have to approve the legislation. If the House, as expected, approves the $9 billion flood insurance proposal, the Senate plans to move quickly in hopes of approving the aid on a voice vote Friday.
Boehner's decision Tuesday night to cancel a vote on Sandy aid before Congress ended its current session provoked a firestorm of criticism. Among the most frustrated by the delay in voting is New Jersey Gov. Chris Christie.
"Americans are tired of the palace intrigue and political partisanship of this Congress, which places one-upsmanship ahead of the lives of these citizens who sent these people to Washington, D.C. in the first place," said Christie.
Sandy was blamed for at least 120 deaths and battered coastline areas from North Carolina to Maine. New York and New Jersey were hit the hardest hit by the storm, with estimated damages in New York, alone at almost $42 billion.
The Associated Press contributed to this report.