Autopilot landings are very, very common for commercial airline flights. Autopilots (with the Flight Management System) fly very complex approaches very precisely which really helps with both airspace congestion and reducing fuel burn (i.e. operating costs).
GPS has been certified for Instrument Landing System Look alike approaches for quite some time now.
Anything that impacts the GPS system will impact airline operations.
I am not a pilot but I do work in aviation and have pretty extensive experience with GPS and autoland systems for bigger airplanes.
Here is a link to GPS Landing System info (pretty simple but ok)
GLS - Eric