The GPS system is meant to have in-orbit spares, I think generally the idea was to have one spare per plane, of which there are six. Normally you would have four operational satellites in each plane, so plus one spare, so that would be thirty satellites in orbit with twenty four operational.
As it is, they actually have thirty one in orbit and operational. They've modified the orbits somewhat, so that more than twelve are likely to be visible at any one time, and if your receiver is capable of tracking that many satellites simultaneously it can use them to improve the accuracy.
If they lost a satellite, they would probably just respace the remaining satellites in that orbital plane, which is relatively cheap to do (in fuel terms).
They also have a couple of functional, but retired satellites in orbit, which could probably be re-enabled if they were desperate. The older satellites tended to use less accurate atomic clocks, so they would probably not provide as good a fix, but they would be better than nothing.
The story sounds a bit like scare-mongering, and you can't help wondering if it's been souped up a bit by the writer.