Do it yourself; turn on the garden hose, and try to seal it with leftover fireworks.
That's actually not a bad demonstration, but it's only one of the possible methods.
The idea is not that you'd cram a nuke down the pipe and set it off. That might work to collapse the formation if the geology is just so, but if you could cram an object down the pipe, a cement plug would be just as effective as a bomb (and a lot less radioactive).
So please explain the complexities to me...
So, we have two other options. Detonate a nuke at the wellhead, or drill a parallel bore and detonate it down there. Detonating it at the wellhead won't do anything but mangle the upper ~1000' of the casing and make the leak completely impossible to get to because the top ~1000' of casing is run through the sandy, silty goop deposited there by the Mississippi River. It's something like cheesecake or a thick pudding. You'd have to do a whole bunch of nuclear explosive excavating to get down to where the casing meets something hard enough to seal against. If you want to talk about ecological disasters that dwarf this little popped cork, this is the way to go. You'd have to eject cubic miles of earth to get anywhere with this plan.
Option two is to drill a parallel bore, drop a nuke down the bore, and blow it. The theory (and I stress *THEORY*) is that it would create some kind of horizontal movement in whatever formations are at whatever depth which would choke off the flow of oil. There are several problems with that. First, it hasn't been verifiably tried. This story about the Russians nuking wells is unsubstantiated. With no reliable evidence around which to build an kind of model, there's no way to know if it will work. Second, they're drilling a relief well
anyway, so by the time you get to nuking depth, you're halfway to a proper kill shot. Which leads to the most important part...
We don't know if setting off one or more nukes is going to be a bigger ecological disaster than a runaway well. It may be that nuking the thing tomorrow is somehow less disastrous than letting it run another couple of months. What we do know is that the well is one disaster, and a nuke is another, and combined that's two disasters. And two is more than one. That may seem sort of silly and childish, but it's just that simple. Why go chasing one doomsday scenario with a second one?