House Secretary Shaun Donovan told a Senate Appropriations subcommittee that the administration is still working on a request for a supplemental spending bill to provide the aid and expects to send it to Congress this week.
"We do not have a specific number," Donovan said.
The price tag is expected to be anywhere between $45 billion and $55 billion. Two Senate Democratic aides, speaking on condition of anonymity because the request is still being assembled, put the number in the neighborhood of $50 billion.
"The president isn't going to leave New York, New Jersey or the entire region to fight for itself," Donovan, who is coordinating the government's Sandy recovery efforts for Obama, told reporters after the hearing.
Donovan urged Congress to take action in "the next few weeks" on the administration's upcoming request.
On Tuesday, the head of the Federal Emergency Management Agency, Craig Fugate, said the government's disaster relief fund still has $4.8 billion, enough to pay for recovery efforts into early spring. So far the government has spent about $2 billion in the 11 states struck the late October storm, one of the worst ever in the Northeast.
New York, New Jersey and Connecticut are together seeking about $83 billion in aid. Donovan described that figure as more of damage estimate, saying some of might be covered by private insurance and other already-funded government programs.
Given the recent budget talks and the strong pressures against new spending, Congress is not expected to approve large amounts of additional money all at once.
The storm devastated coastal communities from North Carolina to Maine, killing more than 120 people. New York and New Jersey were hit the hardest.
Obama can request up to $5.4 billion more without hitting a spending ceiling. Several Republicans have said that more than that should be matched by spending cuts in other federal programs.
Donovan said people who lost homes or businesses are waiting desperately for help. He said it would be a mistake for Congress to quickly approve the $5.4 billion as a "down payment" and defer until next year providing additional funding.
"A down payment simply means that these families, these communities are going to be waiting for months or longer to get on with their lives," he said.
Donovan said requiring spending cuts in other federal programs to cover the cost of additional disaster aid makes no sense. "We believe strongly that the country has to come together even in difficult times and stand behind places that have been devastated," he said.
Officials in the affected state expect the fight for more recovery money will last for months and probably require a series of spending bills. They also fear it will fade as a priority next year.