The government agency that deals with large disasters is the Federal Emergency Management Agency, or "FEMA." This is a relatively new agency, formed in 1978 and enacted into law in 1979 by President Jimmy Carter. The purpose of FEMA is to offer help on a grand scale when state and local governments are overwhelmed by need.
When disasters occur, the state's governor must declare a "state of emergency" and make a formal request to the President of the United States, who will then approve or (rarely) decline funding.
Need is assessed by FEMA and one or more of the following branches of the agency may be deployed: National Disaster Medical System (NDMS), Urban Search and Rescue, Mobile Emergency Response Support.
Claims have various stipulations. A link to information from the IRS is below.