Lawmakers are waiting for the White House to tell them as early as this week how much additional money it needs to aid communities damaged by Hurricane Sandy. The number is certain to be large, and it could make the current budget negotiations even more complicated.

With officials in the Northeast now releasing startling figures on the damage and financial effect caused by the October storm, House and Senate aides said they expect the Office of Management and Budget to soon submit an official request for new money for the Disaster Relief Fund.

About $1.9 billion has already been allocated for damage caused by Sandy, leaving about $5.4 billion in the fund.

The growing possibility of an emergency supplemental appropriations bill adds a new challenge for Congress during a post-election session already expected to be dominated by fiscal battles. Amid talks over tax and spending issues, lawmakers will also have to consider multibillion-dollar aid requests from New York and New Jersey, the two states hardest hit by the storm.

“Make no mistake, this will not be an easy task, particularly given the impending fiscal cliff, and a Congress that has been much less friendly to disaster relief than in the past,” Charles E. Schumer of New York, the No. 3 Senate Democrat, said after a Monday morning meeting with lawmakers and his state’s governor, Andrew Cuomo.

Congress has several options for moving a Sandy relief package. A supplemental disaster-relief measure could be part of a catch-all package of overdue fiscal 2013 spending bills, which appropriators in both chambers want to move before the end of this session of Congress. Such a strategy, however, would rile House conservatives who oppose clearing a lame-duck omnibus.

A senior Senate Democratic aide last week said the Sandy aid package also might be part of an extension of the current stopgap spending law (PL 112-175) that expires March 27.

When a disaster relief package is introduced in December, some conservatives will push for offsetting cuts in other spending, a House GOP aide said Monday. Although the Republicans lost a similar battle last year in connection with fiscal 2012 disaster aid appropriations, lawmakers from states hit by Sandy are trying to make a strong case that Congress should act quickly on an aid package.

New York City “will struggle to recover in the long term unless expedited federal funding is supplied,” Mayor Michael Bloomberg wrote in a Monday letter to the New York congressional delegation.

Bloomberg gave an initial estimate of the total cost of the storm at $19 billion and said he expects at least $5.4 billion in federal aid.

New Jersey Gov. Chris Christie has estimated damages to his state at about $29.4 billion but has not said how much the state wants from the federal government. Cuomo earlier this month estimated the Empire State’s costs at about $30 billion over 10 years.

It may be weeks or months before the federal government knows how much it will need to spend on Sandy relief. To some degree, though, key decisions have already been made.

Disaster relief is part of the budget where presidents have direct access to the federal purse. The White House decides what constitutes a major disaster, and once a major disaster is declared, the federal government is on the hook for aiding communities, often picking up 75 percent of the tab.

President Barack Obama has made seven major disaster declarations in connection with Sandy, covering New York, New Jersey, Connecticut, Maryland, Virginia, Delaware and Rhode Island.

Alan K. Ota contributed to this report.