Ok, without getting into the real underlying reasons for this disaster, basically the offloading of externalities on the general public in the form of unsecured risk by corporations, let's just take a quick look at the possibilities and problems.
Methane hydrate crystals, I believe they're called. Zillions of tons of them on the sea floor, enough to power the entire world for probably 50 years with minimal pollution. That's what is causing the real problem for BP. Any attempt to plug this mother is going to run right into them. Stop up the flow and the crytals form by the ton and the oil seeps around them. Open up the valves, and the methane crystals explode into gas like shaking a cola bottle.
Bad news. So, they might manage to stop this one, eventually, at the source, but the real answer might be to just let the oil flow, and put a couple of layers of booms around the source area - say ten miles and twenty miles radius. That's dooable. Then siphen the oil/water slurry into a big floating tank and suck the oil off the top and into a tanker's hold as it accumulates.
This could even become a deliberate methodology for getting the deep oil up safely. Meanwhile, let's think about what we're going to do with all that methane.