You'd presumably get the nukes to the asteroid with conventional chemical rockets, although I suppose some sort of Project Orion propulsion system is not out of the question. That's what you'd want to do once you got there; you'd basically be counting on nuclear weapons as an incredibly energy-dense form of rocket fuel.

There's nothing that comes close to the MJ/kg of a modern thermonuclear weapon.

Sadly we have nothing that comes close to getting a fleet of nuclear warheads far enough to intercept before it’s too close and we shotgun ourselves. Most likely forms of diversion involve years of planning and deployment, and that’s minus the hasty R&D we’d need to do.

For some discussion of the specifics...

https://space.stackexchange.com/questions/7960/could-we-deal...

Nobody said it's easy. But the last fifty years or so are the first time period were the chances of a successful defense are bigger than zero. We have top men working on it: https://en.wikipedia.org/wiki/Asteroid_impact_avoidance

Right now it isn’t easy or hard, it’s impossible. We probably have the tech, but it would need to be ready to launch on detection. Worse, we have shit detection.

So yes, in theory we could divert some impactors, but in practice right now? No. Nukes don’t help either.

We could blow up a couple of nukes in space and watch for radio echos to find asteroids... Well, except that nukes in space are illegal.

Turning a rifle into a shotgun on this case is a good thing, and may completely solve the problem.

But, anyway, unless we wait way too much, it's better to deflect an asteroid than to break it.

>> How would we get the nuke to the asteroid?

Oh, it's simple- we'd sent in Bruce Willis [1].

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[1] https://en.wikipedia.org/wiki/Armageddon_(1998_film)