With recent reports that the casing of BP's Mocando well has been irreversibly breached and that the mixture of pressurized fossil products from the oil reservoir is carving its own paths through cracks in the seabed, it seems that this disaster has exceeded humankind's ability to stop the flow. Without the ability to cap the original well, the relief wells aren't going to be much use. The use of explosives to try to seal off the shaft might just release innumerable other weak planes for the gusher to exploit.
At this point it appears that an enormous undersea engineering effort will be needed to somehow corral a wider area of gushing oil and gases and siphon those substances where they can be safely processed without spreading out across the open sea. The idea of stopping the flow is probably not the a realistic hope at this point. Sequestering the area of contamination is likely our best hope. I have no idea how to do that, but we're probably talking about a semi-permanent installation of about 30 or 40 acres of material stretching a half mile from the sea bed to the surface, secured against currents, pressures and storms, along with all the equipment needed to capture, separate and process the contained sludge.
UPDATE: Good news. It now appears that the well casing was not breached and that a plug was successful, allowing the well to be permanently sealed from one of the relief well shafts. Also we're seeing mixed reports about what has become of the oil already released into the gulf. For an overview of the issues, I recommend finding a copy of the October 2010 National Geographic.