The problem with building a fence is that, although it stops casual crossings, it isn't a significant deterrent to efforts to cross the border, and it can't be erected as a "set it and forget it" solution. Any kind of fence you might build would have to be maintained, and it would have to be monitored 24/7/365 by surveillance methods that, either directly or indirectly involve human agents who are both in position, and equipped to make interdiction.
In more urban or suburban areas, fences are effective at stopping casual crossings, but a cursory scan of headlines going back over the past several years will net you story after story of tunnels being discovered crossing the international border, and you just can't set a fence foundation deep enough to stop that. You make it 100 feet deep, and you'll find tunnels at 110.
To be quite honest, I wanted a fence myself for several years, but consideration of the manpower issue has set me back off of that idea in all but populous areas. You look at the Berlin Wall; as impenetrable as that thing was, it still had to be manned 24/7/365 along its entire length. Who are we fooling to think that a border fence constructed with opposite intent would require any lesser degree of monitoring? Yes, so the bulk of monitoring function could be wired electronics and sensors, but the glaring reality is that all of those sensors can be set in place without a fence to hang them on, and they all still need to report status to some adequate number of human beings tasked with monitoring them and responding to breaches.
Since that is the reality of the situation, I think it would be smarter to just put the well-equipped humans in position 24/7/365, set up arrays of solar-powered sensors to give them real-time information about border activity, and forego the expense of erecting thousands of miles of fencing. If we did it that way, we could even get a good number of tree huggers on-board with tougher border enforcement because these methods don't create a conspicuous eyesore that slices across the landscape.
Finally, human monitors could be dispatched to the border in a matter of days, and sensor networks emplaced and functioning in a matter of weeks. By contrast, there is no reason to hope that a government-built fence — eve if it were begun today — would be complete by the time my toddler graduates High School.
The bottom line is this: Gov. Perry isn't out of his tree in dismissing the idea of fencing off the entire southern border; the arguments backing him up are pretty compelling, and that is something you've got to admit even if you don't come to the same conclusion that he has.