The debate is about asteroids vs. comets. Asteroids are solid bodies of rock and there are about 1000 of them with diameters of 1 km or more that cross the orbit of the earth. They are called "Apollo" or "earth crossing" asteroids. The "American School" of astronomers believe that these objects are the main threat to earth and humanity and they are concerned with finding them, tracking them, and working out their orbits. This school believes that if all these asteroids can be mapped, and any "bad ones" dealt with, Earth will be safe for the foreseeable future. Their estimates are that we only get hit with one of these babies about every 100,000 years or so.
At this point in time, the American school of astronomers has already found and tracked about 700 of the estimated 1000 such asteroids and, so far, none of them are likely to hit the earth anytime soon. By the end of 2008, they expect to have located 90% of these potential threats.
Of course, they aren't talking about objects smaller than 1 km because they are believed to pose much less risk even if they do smack into the earth.
So it is that the "American School" believes that they can, over time and with superior American technology, survey everything around us and keep our space in space "under control."