The government's plan was pretty stoopit.
They just drop a text and a message on the TVs of the survivors they picked telling them they are chosen without any warning ahead of time. They are taken by surprise. That's not ideal. If they had a plan for this scenario you'd think they'd give the people a little bit of a heads up so they would be prepared.
Also, the way they did it, word was bound to get out quickly. Guaranteeing traffic jams and fights and chaos at the base. They could have let the chosen know ahead of time about some kind of code that would alert them to get moving, but secretly.