The "mud" is not what we think of as mud. It's a dilatant drilling fluid. Dilatant meaning it dilates by thickening. It thickens, increases in viscosity, when shear forces are so great they slow the ability of liquid particles to squeeze between solid particles. The mass seizes. He gives an example of cornstarch, a dilatant material. (His part starts at 1:42 minutes.)
Below he explains why he thinks BP stopped pumping yesterday: "I think they ran out of mud," that is, drilling fluid. (I believe he said the diameter of the pipe from which the oil and gas are spewing is 21 inches in diameter. That's a lot of mud.)
He also describes what a "junk shot" is. He gives an example of stuffing a tube with inexpensive junk, rubber and fiber. When you try to push fluid, especially dilatant fluid, through the labyrinth of junk, it gets stuck. You clog the tube.
He notes how difficult it is to push junk through a flexible hose a mile under water. You risk getting your own input lines clogged.
The reason we're drilling down there in the first place? Says Nye: "We want this stuff," and with hundreds of thousands of oil wells around the world, "it's time to regulate."