Saphroneth
Banned
Basically this, remember that the first thing in my proposal is considerably nudging it by applying tangential force with a lander, if it works, the second, more desperate measure of whacking it with the biggest nuclear hammer we had is not needed.
Plus this, it would sent many fragments hurtling, but instead of being shot with one big caliber rifle, we will get shot by shotgun if the worst come to worst, and in best scenario, the sheer energy of the explosion vaporated most of the ice and materials, and blown it veering completely missing earth.
And yeah, gigaton range nuclear explosion, stick twenty Tsar Bombas here, or launch twentry rockets with twenty tsar bombas,
To get the force for a lander you'd basically need to get the biggest rocket we've ever launched out of Earth's gravity well there without it having expended any fuel.
It would take TWENTY FIVE Saturn V launches to get one Saturn V into Low Earth Orbit. And each one (which I remind you we can't make these days) cost about 3.5 billion in present dollars.
So to get one Saturn V rated delta-vee causing device to LEO would take over twice the total cost of the historical Saturn V program even if we had as much time to work on it.
To get one Saturn V to TLI (Trans Lunar Injection, a more realistic delta-vee requirement for the thrust lander) would take sixty-one Saturn V launchers, or
This is not a turnkey solution.
And as for the "stick twenty Tsar bombas" - we don't have any.
There has been an analysis which decided that one gigaton of blast would suffice to handle a 1km wide asteroid/comet, but that analysis was conducted after the Shoemaker-Levy 9 impact. (And it was all hypothetical - the meeting was to design such a device.)
The most likely launch rocket is probably the Energia - though the problem is that that failed once (third stage start problems) and succeeded once, and it has less boost heft than the Saturn V.
Overall result...
It might be doable. But it would most certainly not be a sure thing.