The US may turn off the GPS system / make it unusable. On the same token they may also ban flight by non military aircraft and enforce it in another country (eg parts of Australia as opposed to parts of Iraq). Given the dependency of the US's economy on GPS the second option would be far more palatable to the US public.
If the GPS signal is not available procedural separation could be used. It is no where near as efficient (or dare I say it as safe) as a radar / ADSB environment. A fire, a bomb, a failure of both primary and secondary power supplies, a SSR failure at either ML centre or BN centre would be far more disruptive than the loss of the GPS signal. If the GPS signal is jammed locally for war like or terrorist reasons I don't think any civilian aircraft would be allowed to take off (at least initially, and then ADIZ procedures would apply with extremely limited aircraft movements) so it becomes a task of getting the flying aircraft down safely. The ATC's out there should be able to give us an indication of whether the controllers on a shift would be able to cope with the additional workload by effectively halving the number of aircraft to be dealt with (hang on a sec most of them seem to be in on the conspiracy).
FB - Are you suggesting that I should throw away my 406 GPS equipped PLB on the remote chance the US disrupts the GPS signal in case I ever need to use it?
SSR is not spoof proof either. I've been in command of two different aircraft (about 15 years apart) where the indicated altitude to ATC is nothing like the actual altitude. A clever electronics engineer could easily alter the returned distance and / or altitude (multilateration would be able to be programmed to detect distance spoofing). Jamming primary radar would be quite straightforward as well.
It doesn't take much technology to upset ground aids either - I would be extremely surprised if even our military doesn't have the necessary equipment to do so - most electronic engineers could design and build gear to upset individual navigation aids in their sleep mainly using gear that can be brought off the shelf - and if they wanted to build from scratch even DSE would sell all the necessary components.
The necessary information to spoof these systems is publically available - probably not all on the internet but it could be found. No I am NOT going to say how on PPRUNE - that would make it too easy for a terrorist.
Have to go - more to add.