You want the time. Simply put, for that the minimum requirement is position (and hence the distance) and velocity. To know the position you need to detect it. Once you detect it, you can calculate the trajectory and thus the time you have to settle your issues (assuming it is on a collision course).
I got this from CNN:
The B612 Foundation is building the Sentinel Space Telescope, the world's most powerful asteroid detection and tracking system, to see the millions of asteroids we can't see today and could pose threats to our planet.
Also, NEOSSat, the Near Earth Object Surveillance Satellite, is a micro-satellite launched in February 2013 by the Canadian Space Agency (CSA) that will hunt for NEOs in space.
Tracking systems are recording asteroids even as large as 140 meters. Any asteroid with a radius more than 300 meters means an assured global catastrophe. Check this out. The size that you are asking about is so big that it will create noticeable gravitational effects (like perturbation in orbit) and so we will know about it.