In the movie Armageddon (1998) NASA isn’t able to detect the asteroid movie until it’s 18 days away from Earth, which is absurd. Granted, Armageddon is possibly the least scientifically accurate movie in history, but that aside…when should they have discovered it?
The movie says it’s “the size of Texas“. Let’s call it 1000 km in diameter, about the size of Ceres. We’ll also presume that it’s coming in on a trajectory similar to other extra solar asteroids, so 26 km/second.