Darwinists often state something along the lines of: "If human beings in a relatively short amount of time can breed several varieties of dogs/pigeons/roses, just think of what nature can do given the vast span of 1 billion years!" The underlying principle seems to be that intelligence working over a short period of time has little chance of prevailing over an entire universe with eons of time available to it.
But, really, this makes no sense at all. Let's look at an example. A human being can in very short order place a pack of cards in order. By the reasoning mentioned above, it should be the case that a big enough assembly of blindfolded card shufflers should be able to perform the same task, given enough time, since nature and time handily beat intelligence working over short periods.
So: the odds of getting an ordered pack of cards from a random shuffle is 52 factorial, which comes out to 8 * 10^67. Now a human being is composed of about 10^29 atoms, or roughly 10^30 subatomic particles. There are about 10^80 particles in the entire universe. If all of those particles were tied up in blindfolded card shufflers, we'd have about 10^50 shufflers. If each one of them could complete a shuffle in 1 second, it would take about 10^18 seconds to get that ordered deck. The universe has been in existence for about 4.6 * 10^17 seconds (so we're halfway there!).
In summary, if all the mass of the universe had been tied up in blindfolded card shufflers (very fast ones, at that), we still wouldn't have gotten that ordered deck, something that one unblindfolded person can yield in about a minute.
The principle that unguided nature can outperform intelligent action is simply false as a general proposition, and should not be used as part of an argument supporting the Darwinian story.
The fact that human beings can produce varieties through selective breeding is no basis for claiming that unguided nature can. Intelligent agents have an immense advantage over blind nature. If mankind has not been able to breed new species from other species (i.e. selecting catlike characteristics from dogs, eventually yielding a cat), then there is no compelling reason to expect blind nature to be able to do so, at least not based on the argument that "time and variation is all it takes".