The Bush administration has ordered the Border Patrol to move some personnel and equipment from the border to deal with Katrina, NewsMax reports (link):

...According to [the U.S. Customs and Border Protection agency], however, plenty of its scarce resources are now committed to rescue and law enforcement support in the multi-state areas devastated by Hurricane Katrina.

Its fixed wing aircraft are used for transportation and for surveillance/reconnaissance efforts to identify anyone in peril. CBP helicopters are also used in transport and in search and rescue efforts.

The air support efforts are being coordinated through an airborne command center, which includes airborne radar and traffic management capabilities. Marine support is also providing transportation and rescue assistance. And CBP is sending over one hundred Border Patrol agents to provide law enforcement support to the impacted area. As CBP pointed out to NewsMax, its relief teams in the New Orleans area are not by any means gratuitous. The proliferation of ports of entry in the area means that the agency has a large number of CBP personnel regularly on the ground. Many of these CBP personnel were hit by the storm and are in need of relief...

While Katrina was obviously not an attack, perhaps [a definition of the word "feint] might shed a tiny little bit of light on why this is a very bad idea.