Dear astronomers, physicists, and WAGgers of the SDMB:
I’ve read that the original opening scene of the instant-classic Armageddon involved children spotting the planet-killing asteroid in the sky. Assuming they’re looking at night without a telescope and the space rock is visibly distinguishable from a star or planet, how long might the human race live to worry about such things?
…need answer fast…for, um…no reason. ::looks up:: 
A lot depends on how big it is and exactly which way it is traveling.
You could end up with a planet killer that gives pretty much no warning whatsoever. Just one day, WHAMMO. This is especially true of objects that come from a direction close to the sun, as the sun is going to pretty well blind us from seeing them until it’s too late.
On the other hand, if the object is basically following the Earth around the sun in very close to our orbit, it may slowly come up behind us and could be visible for quite some time.
Also, the bigger it is, the more visible it will be. You only need a certain size for it to be able to basically wipe out life on Earth as we know it. But you can easily have objects that are larger than that, and those will be visible from much further away.
But I can see this at night. Let’s say midnight, and it’s not near the horizon. It’s at an elevation that an actor would point at.
That’s no moon, it’s a space…er, asteroid! So smaller than a moon.
In almost all cases, you’ve got a few minutes to live after you can see it as a disk.
Venus at its closest to the earth is a little more than one arc minute in diameter. You’re supposing that the asteroid looks larger than Venus. Let’s be generous and say it’s 1.5 arc minutes at the point where it clearly looks larger than Venus (actually I think it would probably need to be several arc minutes in diameter for the average observer to notice the difference). Let’s also be generous and say it’s a very large asteroid, 10 km in diameter, about the size of the Chicxulub impactor, so we can see it as a disk from far away. For a 10 km object to have an angular diameter of 1.5 arc minutes, it would need to be 10 km / sin(1.5’) = 23,000 km away. Asteroid impacts on earth average about 17 km/s. The absolute minimum impact velocity would be Earth’s escape velocity of 11 km/s. Let’s take that lowest value to give us the most time. That would give us about 35 minutes to impact. Smaller or faster asteroids would obviously give us less time than that.
Considering that a previously unknown meteor passed near enough to me to be observed in several states recently without warning, I’d say that the chances of avoiding such are nil, if it’s targeting your backyard.