Are mutations enough to explain natural selection?

The way I understand this issue is that it's sort of like compound interest at the bank: a very slight advantage carried over a thousand generations, say, translates into a major spread through the population. If that one-meter-further flight resulted in 0.01% more of the possums that could do it surviving to breed, the trait (assuming it's heritable, of course) would take over surprisingly soon. And nature isn't in much of a hurry.