In a statement, the four Democrats -- Kirsten Gillibrand and Chuck Schumer of New York, and Robert Menendez and Frank Lautenberg of New Jersey -- said they expect more supplemental requests will be needed, The Washington Post reported.
In a letter to Congress, Obama asked late Friday for $60.4 billion.
"This is going to be a tough fight in the Congress given the fiscal cliff, and some members have not been friendly to disaster relief," the senators said in a statement. "But the care with which the package has been put together has given us a good head start."
The governors of the two states, Republican Chris Christie of New Jersey and Democrat Andrew Cuomo of New York, issued their own statement thanking the president.
Congress could take up the aid request next week, the Los Angeles Times said.