I guess you never tried dropping pebbles in Old Faithful from an airplane to stop the geyser, have you?
Okay, look. The oil reservoir is thousands of feet below the lithic surface. The Ivy Mike test, a ten megaton release, only gouged out a 150 foot diameter crater. A small bomb, like in the Hiroshima/Trinity size I specified, would fracture the near surface rocks and not have a chance of penetrating the oil reservoir. But it would turn off the oil.
And which has the worse ecological footprint, a small controlled energy release with a clean modern weapon, or a perpetual oil leak that currently cannot be contained by available technology?
To put it in simpler terms, is it better to kill a thousand miles of coastline after a summer of uncontrolled oil leaking, with the inevitable extermination of coastal ecosytems, or to make a short blast that will kill some wildlife locally but have little long term impact on the Gulf ecosystems?
If they can put a robot on the gushing well head, they can place a nuclear explosive exactly where it needs to go.
Chemical energies would not be sufficient to ensure closure.
What will killing all the fish in the Gulf and all the sea floor marine life with an unlimited oil spill do for the Gulf fishing industries?
There's enough oil leaking that there's a reasonable chance that the Gulf Stream might deliver some of BP's oil to the British shores without the hassle of using a tanker.
It might even be true. The effects of explosives unter 2200 psi of hydrostatic pressure isn't widely published, and maybe it would work.
For the purposes of this discussion it is assumed that chemical explosives are insufficient to the task.
The real issue is whether people are so afraid of the nuclear boogeyman that they're willing to sacrifice thousands of miles of pristine coastal ecosystems and the national economy to avoid doing something simple that would cost less, far less, in real terms by any measure.
So far it looks like the mental conditioning against the nuclear boogeyman is stronger than a desire to preserve and protect a thousand miles of wildlife preserves.
I'm not equipped with the knowledge to answer the question. I do know the Russians were successful several times but they never did it this far underwater under these conditions so probably no.
If I'm not mistaken, the pressure coming out is greater than the pressure pushing down, it could make it worse.
In my amateur opinion, it's to risky to attempt.
I was discovering that life just simply isn't fair and bask in the unsung glory of knowing that each obstacle overcome along the way only adds to the satisfaction in the end. Nothing great, after all, was ever accomplished by anyone sulking in his or her misery.
It seems like this question should be answered by someone with expert knowledge in this field, instead of anyone of us, or a politician.
"To waste, to destroy, our natural resources, to skin and exhaust the land instead of using it so as to increase its usefulness, will result in undermining in the days of our children the very prosperity which we ought by rights to hand down to them."~ Theodore Roosevelt (Message to Congress, Dec. 3, 1907)