I also happen to think that within a moment of crisis, it's rather unusual for the populace to rebel against their leaders. The mistake GTVA made was to go wrong on their calculations on the Shivan threat. But they were always well aware of this blindness (listen to Petrarch's command briefings where he warns of the danger of miscalculations here), they designed contigency plans (some more successful than others) and the risk did end paying off (gathering sufficient intel for the duplication of the Knossos portal). FWIW, the GTVA never had a real chance even if they calculated correctly the danger from the very beggining, since they would have tried to shut down the portal and just wouldn't be able to (see Flaming Sword). Further, it could have been even more dangerous, for they would (a) probably not understand they didn't close the portal sufficiently for a Sathanas not to enter it until it was too late, (b) not have any heads up for the Sat Fleet coming down, (c) generally thought they were safe and ok.
As it were, they started evacuating Cappella right from the get go and never ceased to do so until the end. They did alright, given the circumstances, and they did manage to save hundreds of millions of lives, the Knossos intel, etc. AFAICS, they shouldn't have many political problems on their own (here I disagree slightly with BP canon). The worst problem they would have was for mankind to face itself with the knowledge of the kind of cruel, daunting Lovecraftian cosmos they inhabit. I see a sudden brutal surge of suicide rates, for example, desperate depressions, wild panics everywhere, etc.,etc. It could almost shatter a civilization.