The funding is included in the fiscal 2012 budget bill for the Department of Homeland Security, which administers the government's disaster relief fund. The funding is more than double the amount included in the House-passed DHS budget bill, which would provide $2.6 billion for disaster relief.
It remains to be seen how Republicans react to the funding or if they demand any specific offsets.
The White House on Monday estimated about $1.5 billion in disaster aid will be needed to cover damage from the hurricane, on top of $5.2 billion needed to cover other disasters.
Overall, the Senate version of the budget bill would provide DHS about $41 billion in discretionary spending for 2012, which is less than the $43.2 billion President Obama requested. The department's current budget is $41.8 billion.