For a smaller asteroid the detection becomes more dicey. Consider an asteroid that is only 2 km in diameter with the same low albedo of 0.1. Such an impactor with a mass of 1.59 metric tons and a velocity of 20 km/sec would have the explosive power the equivalent of 1 Megaton of TNT. Its surface can be resolved by a 12" clear aperture telescope at a distance of 589,328 km while its Apparent Visual Magnitude of 4.6 would render it invisible to the naked eye at this distance. Its Absolut Visual Magnitude is 16.6, and a 14" full aperture telescope can see it as a point source of light out to a distance of 1.59 AU, just beyond the planet Mars at 1.52 AU.
Aain, it isn't the detection distances that prevents us from recognizing these threats, but rather the imperfections in the Main Mirror used in the vast majority of telescopes, that skews our orbital calculations based on observations made with these telescopes.
The telescope Manufacturing industry not only decieves us with their substandard products, but actively miseducates us concerning the difference between a parabolic reflector and a paraboloid. Most definitions of a parabolic curve as a conic section are accurate, but defining a paraboloid as the volume of revolution of a parabolic curve is highly inacurrate, as it merely redescribes a parabolic reflector. The endearing characteristic of a parabolic reflector is that it has a continuously variable focal length from its outer edge to its axis of symetry. A paraboloid, on the other hand, only has 2 distinct focal lengths from its outer edge to its axis of symetry, - characterised by the coma producing ridge produced by the seam of the two sperical sections that make up the paraboloid.
Thin Mirror Technology may allow us to see farther, but it does not allow us to see better.  When looking for impactors, we need to see better, not farther.