And so many of these things rely on a fully functional GPS system,
> how long until those who want to bring down Western civilization
> figure out a way to cripple this system by knocking out a satellite?
Not an easy task. There are spares on orbit right now. There [are] several spares awaiting launch.
Someone would have to destroy several widely separated satellites before they would knock out the system. With our technology we would figure out quite quickly where the destruction was coming from. That would be a major act of war.
Here is a link to info about the GPS constellation: