If NASA ever encounters a killer asteroid, it would let people know via a text message. That is actually the first step in the elaborate course of action planned by NASA and FEMA.
Something like 12 scientists or less will get a preliminary text or email. At that stage, very little will be known about the space rock about to hit the earth. But soon, with hundreds of people looking at that thing, things would change drastically.
It is highly unlikely that earth will get hit by a space rock so large that it will cause a global event. However, FEMA is preparing people for “low-probability but high-consequence disaster scenarios”. The odds of such as asteroid striking the earth is very low (5,000-foot asteroid is only expected to hit the Earth about once every 1 million years), and 90% of NEOs or Near Earth Objects over a kilometer in radius is already under NASA’s radar.
NEOs discovered are logged by an organization called Minor Planet Center, which is a public forum. If an asteroid has a chance of hitting the earth, NASA notified the White House Office of Science and Technology Policy, and then soon after, issues a press release to inform the public.
Before that, NASA and the Minor Planet Center must agree that the rock will hit the earth. Since all the trajectories and orbits are available to the public, there will be a lot of internet chatter.
However, NASA plots out expected orbits for NEOs. Most of them are about a hundred years, before they even come close to earth.
Moving an Asteroid
Engineers at NASA has sophisticated plans on dealing with asteroid. These include deflecting or destroying them. Methods include shooting lasers at them, or even blowing them up, just like in Armageddon.
None of the methods are yet tested. But theoretically, they work. NASA is also working along with ESA on Asteroid Impact and Deflection Assessment (AIDA), which will test if an asteroid can be moved using an impactor.