Interestingly, the military GPS signal is encrypted using what is called the A/S "anti-spoof" code. Which was deployed in the '70s. So you know they've been thinking about it for quite some time.
Practically speaking: Assuming one can shield the spoofer receiver from its own transmitter there's no real reason why a spoofer can't set up a receiver at one location and rebroadcast the encrypted signal as received there. If rebroadcast at sufficient power it would easily overpower the true signal, and would indicate the spoofer position rather than true position everywhere it was the strongest signal. Sort of like if you just moved everyone's antenna to the spoofer location using a very long antenna cable.
It would be very interesting to know what military receivers do to mitigate such an attack. I haven't seen anything in open literature. I suppose it would be (rightfully so) classified technology.