Proponents counter that the depth at which the explosion would occur could prevent that possibility.
"If you go deep enough underground, nothing gets out," said former Air Force Secretary Hans Mark, now an engineering professor at the University of Texas at Austin specializing in national defense policy.
Mark and others point to the former Soviet Union's strategy of capping out-of-control gas wells with below-ground nuclear explosions.
But others argue that the fact that the BP well is an oil well -- not a gas well -- and that it is underwater (unlike the Soviets' gas wells) make the situation too different to be comparable to the Soviet experience. There's also the Soviets' not-so-reassuring success rate: though the U.S.S.R. successfully plugged four gas wells with nuclear explosives, its last effort in 1981 failed.
"A 20 percent failure rate is way beyond anything that would be acceptable here," said Fischbeck.
Choosing a nuclear explosive, in particular, could land the U.S. in a diplomatic pickle, nuclear policy experts warn.
"The United States has signed a treaty that we would not explode nuclear weapons under water or anywhere else," said John Isaacs, the executive director of the Washington, D.C.-based Center for Arms Control and Nonproliferation.
The Comprehensive Test Ban Treaty, which nations began to sign in 1996, puts a moratorium on nuclear weapons testing. Were the U.S. to run afoul of the treaty, experts say, states like Iran might use that to justify their own nuclear weapons exercises.
Brownfield argues that conventional explosives could be used instead and so does Clinton.
"You don't have to use nuclear weapons, by the way. I've seen all that stuff, just blow it up," the former president said at last weekend's media event.
But not everyone -- including proponents of the explosives idea -- is so sure. Mark says it would take larger conventional explosives to match the power of nuclear ones, and they might prove trickier to transport.
It's a "problem of getting to the pipe," he said.
"You'd have to get very close, and you'd have to be very lucky."