Re: Throwing theories gets us there
I think the most extreme example would be A/2017 U1 (search: A/2017 U1 Pan-STARRS).
With our current monitoring system that 400 meter long space rock traveling at 25 kilometers per second (100 m–1,000 m × 35 m–167 m × 35 m–167 m @ 94,800 km/h) would have hit us without warning.
But consider it's path (nasa has a nice animation). It came at us from the most unlikely and least monitored direction.
And we did see it even if it was only as it was leaving.
But for the largest and most likely threats humans have very good monitoring and are already tracking some objects that will not be a threat for decades or hundreds of years.
As for lead time NASA claims it needs 5yrs but keep in mind that NASA is not the only expert agency. Other nations have landed on far away asteroids, and have more recently landed on the moon. We are ready and getting more ready as long as we can keep on advancing and avoid another dark age.
For more and more accurate information search: B612 Foundation.