I'd argue that for critical infrastructure (on land), there is zero dependence on GPS. For anything that is connected to the internet, accurate time is usually provided by NTP (Network Time Protocol, invented in 1981). Very robust, distributed, and well thought out. A bit simplified, an NTP server without it's own time source queries a set amount of sources, and choses the most reliable one based on various criteria, and then propagates that signal. If one or two of many sources is a gps receiver, it will have no impact at all. GPS time signals are relatively novel, and any sensible system administrator running an NTP server would use mostly land-based atomic clocks, such as
http://tycho.usno.navy.mil/what.html, they're still considered the gold standard ("The primary facility, in Washington, D.C. maintains 57 HP/Agilent/Symmetricom 5071A-001 high performance caesium atomic clocks and 24 hydrogen masers. The alternate master clock, at Schriever Air Force Base, maintains 12 cesium clocks and 3 masers. The observatory also operates four rubidium atomic fountain clocks, which have a stability reaching 7×10−16").
Most consumer devices are set to use a "lower level" (stratum in NTP terminology) time server, eg an NTP server run by Microsoft, Apple etc. which again uses multiple sources. The worst thing that can happen in case of a GPS time issue, is that clueless people who use only GPS will have the wrong time until someone tells them what to do. I can't see how it would affect critical infrastructure though.