Earlier quoted context omitted.
H-bombs are sitting on tops of 30-year old space rockets right now. Sending them to defeat asteroid might be even more devastating than not sending them though.
ICBMs don't even make it to orbit - if you wait till an asteroid is close enough that an ICBM could hit it then you might as well not bother. [NB I do know that the SS-25 could do fractional orbits.]
Now whether or not such a solution would actually work is another matter. The original comment however was "extremely high tech such as H-Bombs on rockets". Both are examples of tech that's decades old.