Asteroid 1950 DA is calculated as the highest probability of impact with the Earth for any near Earth asteroid to date: about one in 300. This will be in March 2800. If it hits, this is bad news. Very, very bad news, particularly if we haven't figured out how to destroy it first.
I'm not a gamblin' man but I'm willing to stake good money on Humankind's ingenuity prevailing over the next 798 years.
And if we DO have such a device by then, we could simply transport the asteroids directly out of the path using the combined oomph of our mighty, mighty laundry transporters!