http://en.wikipedia.org/wiki/Kessler_syndrome
http://webpages.charter.net/dkessler/files/KesSym.html
"today, the catalogue contains about 13,000 objects, or more than 3 times as many objects. This gives a collision rate that is more than 10 times what it was just over 30 years ago, or 0.13 per year….which is the same as one catastrophic collision between cataloged objects every 8 years….with the time between collisions rapidly becoming shorter as the catalog continues to grow. The larger fragments from either explosions or collisions will further accelerate the rate of collisions."
Without that system, we're back to compasses, line of sight and dead reckoning. We lose the current insane advantage of realtime positioning anywhere on the planet.
That's 1 18 satellite system - and we absolutely can't run a modern civilization without it.
Also, GPS satellites are in medium Earth orbit, which is rather sparsely occupied. In a Kessler syndrome scenario, GPS would likely survive.