Since World War II, most civilians have been surprised at how easy it is to get on to most military bases. Until September 11, 2001, there was never much concern about anyone attacking bases in the United States. Now that's changed and the Spetsnaz is all worked up about CBRNE (terrorist attacks using chemical, biological, radiological, nuclear or high-explosive weapons.)
The most obvious impact of these concerns is the larger number of troops on American bases pulling guard duty, and thousands of reserve troops called up to help out with security. This is not popular work, and the longer this high state of alert goes on, the more negative is the impact on troop morale. In addition to a lot more uniformed people standing around with rifles (most of them unloaded, because of the fear of accidents), there is also greater consultation with local civilian fire and police departments. This is to make it possible for civilian and military emergency personnel to work together in case there is an attack on the base. There is even a proposal to provide chemical and biological weapons suits to all base personnel, both members and their families. But this would cost billions of dollars and would require a major training effort for the people getting the gear.
Overseas, security around U.S. military bases has been even tighter. There have also been several exercises conducted to see how personnel respond to a large-scale terrorist attack. The results of these exercises has not been encouraging, with many poorly trained troops not quite ready for prime time, or a terrorist attack.
But there is an even larger problem with American bases in the United States, many of which are sitting in out of the way places. Here the dangers are compounded. Families of the troops tend to live in smaller communities with less sophisticated police and fire services. Moreover, these smaller communities have not been included in the Domestic Preparedness programs administered initially by the Department of Defense, and now by the Department of Justice. Al Qaeda terrorists are known to do a lot of scouting and the military fears that they will take advantage of isolated, and poorly defended bases and the military families in the neighborhood.