[quote=Grothnor]
Building off Rax's ideas, the guys we ran into could have been advance troops/scouts. Their full army could arrive later enough that we have plenty of time to recover, but we'd still be stuck in the hospital/safe-zone.
[/quote]

A hospital might not be the safest place. In fact, any place that masses of people converge onto will become a target, strategically speaking (if I was an alien invader that's what I would do). It would be best to get out of the city, or at least as far away from the downtown area as possible, toward the outskirts. 

Simultaneously the invasion could be happening in other cities around the country, and though we escape we come to another place only to find the same kind of destruction and chaos. 

Also I've been thinking that we're going to need some kind of significant advantage in order to have a chance of making any kind of difference. Like, we're gonna need something that our country's military force don't have, and I'm thinking it should be some kind of alien weapon. Perhaps personal cloaking devices/force shields, or teleportation devices. It's gotta be good and it's gotta help us get past their defenses in ways that an ordinary soldier wouldn't be able to.