Obama issued federal emergency decrees for New York and New Jersey, declaring that "major disasters" existed in both states.
Power outages darkened large parts of downtown Manhattan. A large blaze destroyed more than 80 homes in New York City's borough of Queens, where flooding hampered firefighting efforts.
"To describe it as looking like pictures we've seen of the end of World War Two is not overstating it. The area was completely leveled. Chimneys and foundations were all that was left of many of these homes," New York Mayor Michael Bloomberg said after touring the area.
Neighborhoods along the East and Hudson rivers in Manhattan were underwater, as were low-lying streets in Battery Park near Ground Zero, where the World Trade Center once stood. Lower Manhattan could be without power for four days.
One disaster modeling company said on Tuesday that Sandy may have caused up to $15 billion in insured losses. That would make it the third-costliest hurricane on record, behind hurricanes Katrina, which laid waste to New Orleans and the Gulf Coast in 2005, and Andrew, which devastated parts of Florida in 1992.