GPS isn't affected by demand, as it is transmitting only from satellites, and the receivers only receive, they do no transmit to the satellite at all. At best, there is a slight degradation by having antennas in really close proximity. A million man march, each with a GPS device, might cause some degradation as each device will absorb a bit of the energy that others might. If it were to happen, it would only absorb the signals at low angles, which aren't really required, although they do help to get a better solution. There could also be some noise generated, as receivers can transmit a very small amount of signal in the range of the intended signal as generated by their oscillators. But in large part, it won't be degraded, and at worst case, would only be reducing the number of satellites slightly. And even that effect is probably more due to the large number of people around you, and not the electronics which they possess.
Differential GPS, on the other hand, might have some degradation. This requires that GPS corrections be sent out, and the network traffic that these are sent out on might not work as well. Still, that would only lead to uncertainty in the highest order, it would still be able to figure out which street you are on.
From the article comes the following quote:
print out directions since GPS (especially Google Maps) likely won’t be an option
Many people associate GPS with turn by turn directions from something like Google Maps. And that has the potential to be really affected. I suspect the author made the same mistake.