The big question from theoretical physicist and occasional blogger Dr. Michio Kaku isn't "Can we terraform Mars for human habitation by bombarding it with comets and asteroids" but "Why haven't we started yet?" After appearing on the Sci Fi channel to explain his idea, Kaku took to his blog to answer reader questions about what, exactly, he was talking about. He begins by dismissing the idea of terraforming Mars with nuclear power plants as the reckless insanity it obviously is, going on to explain his much more modest idea of shooting asteroids at the red planet's surface:
In the program, we mentioned that it might be possible to heat up Mars using nuclear power plants, but this would be a very slow, expensive, and perhaps dangerous plan. A much faster plan would be to divert comets and meteors to Mars. We also mentioned that, if you aim the comet or meteor carefully, you can control its orbit. This means you can gently have the comet or meteor enter Mars orbit, and then slowly descend to the surface as the orbit decays. This means that much of the comet or meteor will burn up in the atmosphere and release water vapor. The point here is that we can accurately aim the comet or meteor so that we can minimize surface damage but maximize energy transfer, which is what we need to heat up Mars.
Kaku goes on to set up a timeline for terraforming Mars. He predicts the first astronauts will arrive "mid-century," the first human colonies will be built "later in the 21st century," and terraforming will happen in the "mid 22nd century." Just to give a sense of scale, 2250 is 240 years from now; the date 240 years ago was 1770. So, according to Kaku, the distance between the American Revolution and today is roughly equivalent to the distance between today and the terraforming of Mars. Given how little things have changed in the past two and a half centuries, that may not be as far off as it seems.
As a mind-bending bonus, here's a video of Kaku discussing "time pretzels, cosmic music, and the theory of everything."