From Media Matters:
The December 2004 National Response Plan (NRP), the federal Department of Homeland Security's (DHS) most recent plan for coordinated federal response to disasters
http://mediamatters.org/rd?http://www.dhs.gov/interweb/assetlibrary/NRP_FullText.pdf , confirms the Red Cross' status as a "primary agency"
http://mediamatters.org/items/200509090002#establishes that will, under the oversight of FEMA and DHS, coordinate "federal mass care resources" to affected areas. Moreover, in a "catastrophic event," such as what befell New Orleans, the NRP directs FEMA
http://mediamatters.org/items/200509090002#directs to act on its own authority to quickly provide assistance and conduct emergency operations, bypassing state and local authorities if necessary.