Spin that asteroid!

I have to wonder about the accuracy of measurement of where an asteroid may land on the Earth once said asteroid is spotted and plotted. If the measurement is off by a millionth factor does that mean that the impact, instead of mid-Pacific, is mid-Atlantic? And if you choose the wrong direction or thrust 2, 5, 10 years before impact, that you doom a new set of people, but doom none-the-less.
 
Here’s an idea I have not heard yet. Send a spacecraft to the bolide (yes, yes, takes years I know). But once there the craft anchors itself to the rock — with a tether — and then starts to produce angular thrust to spin the asteroid around some point off center of mass. Faster and faster the asteroid-rocket will rotate. And then when the asteroid gets close enough to know much more accurately where the rock would impact — the tether is cut and the angular momentum now forces the rock to “streak” off like a pebble from a sling (streak being a relative term here) thereby missing the Earth or landing in some underpopulated area. Imparting counterbalanced spin gives humans a bit of power over the asteroid — to be wielded upon demand.
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