If the coin is biased so that it lands on heads only 1 in a million times it will take a lot of coin throws to get some randomness out of it. This isn't a limit of the technique, just a consequence of the low entropy source.
The latter (except that it doesn't always have to be long; the length of time per bit follows a gaussian distribution). If it were the former then randomness would be predictable in some sense. It's similar to the halting problem.
