Not likely. They had to be able to work at that level to be able to put the well-head in in the first place. I think the biggest problem with most well blowouts is fire or the danger of fire, which isn't likely to happen at the bottom of the Gulf.
This is NOT to say that fixing it will be easy, but the technology doesn't have to be developed "from scratch".
Its already on fire.
They got a real problem. If the casing is bent over they have to cut the casing and then either drive a jacket over that casing or thread it and get a valve on it to seal the thing.
It all depends on the pressure at the head I suppose.