I'm certainly no astrophysicist, but astronomy, along with cosmology and quantum physics, have long been a hobby of mine.
Generally speaking, anything with the velocity of a typical asteroid will blaze by an object the size of the earth in a matter of about fifteen to twenty minutes or so. Add to that the mass of such an object, which adds to it's momentum, and chances are rather slim. This rapidly changes if the object is close enough to interact with the Earth's atmosphere, which then imparts enormous drag and friction, and dramatically decreases the object's kenetic energy (not to mention creates quite a show).
Bottom line, unless something like this is coming straight at us to start with, chances of the Earth "snagging" it are slim. Gravity is a terrifically weak force, although, since it is only accumlative (unlike the other three fundamental forces of nature), it overall is the most pervasive and influential.
It's always pulled in by Earth's gravity, and vice versa.
The real question: What did Bush know and when did he know it?
--Boris