There is certainly an inner drive, more pronounced in women, because species without such a drive don't make it though natural selection.
Really? The reproductive urge in humans seems to be more centered on a desire for sex rather than on a desire for children. And, in most animals, this is sufficient; sex leads directly to reproduction without the brain having to take an active role after the exchange of genetic material takes place.
Humans, oddly enough, seem to have evolved adaptations for ensuring that people have unplanned pregnancies in spite of their big brains. Human females don't have an obvious estrus cycle, their fertile periods are often unpredictable, and each individual act of copulation has a relatively low chance of causing a pregnancy. As a result, humans are often willing to have sex when they don't want children and end up having them anyway.
There is certainly an inner drive, more pronounced in women, because species without such a drive don't make it though natural selection.
A developmentally complex species needs a drive to care for offspring. A simple species just needs a drive to reproduce.
ETA: What Lumifer said
Haven't had one of these for awhile. This thread is for questions or comments that you've felt silly about not knowing/understanding. Let's try to exchange info that seems obvious, knowing that due to the illusion of transparency it really isn't so obvious!