The sooner those claims are filed the better, but that doesn't necessarily mean everyone will get what they ask for.
One of the concerns, as pointed out by the Consumer Federation of America, is that there may not be enough money in the pot to cover everyone:
Payments by private insurers for wind damage to homes and business properties from Hurricane Sandy will likely exceed $10 billion dollars. Flood claims paid by the National Flood Insurance Program (NFIP) will be at least $8 billion dollars and will likely exceed $10 billion, exhausting the NFIP’s existing $4 billion in payment authority. To make up this shortage, FEMA is authorized to borrow up to $500,000 with an additional $1 billion available with Presidential approval.