If there's one trend that you cannot extrapolate, it is this one.
1. Women are pursuing education and careers, which means they're often already thirty before they're "ready" to have children -- leaving no time to pump out more than one or two
2. Children are getting more expensive, both in terms of the absolutely compulsory costs and the things you're just expected to buy for them
3. For people who expect to get around by car, more than three children is a nightmare. In fact, with all the modern safety regulations having more than two children is a nightmare. My parents were happy to cart around three young children in the back of an early 80s Mazda 323, but you couldn't do that any more because a minimal child seat would take up nearly the whole back seat
4. There's really no incentive to have more than two children any more. Child mortality is nearly zero, and it's no longer expected that children will support their parents in their old age.
I am kidding, of course -- I doubt too many people these days have children for purely dispassionate economic reasons, but we shouldn't pretend that those considerations don't enter into the equation, and aren't entirely legitimate.
As the youngest of three, I'm well aware of what a great idea it is to have more than two children. ;) (And no, none of my own just yet, but I'll probably have two so that I can avoid owning a minivan...)
If there is something in society that causes women not to want to have kids and this remains in place then the prediction is correct.
This is a nature versus nurture debate.
Your interesting and pertinent question has both an easy answer and a hard answer. I'll provide references for both.
The easy answer is that this behavior is "heritable," that is that correlations in rank order on this dimension of behavior are stronger for close relatives than for persons who are not close relatives. That is true of ALL human behaviorial characteristics, without exception. A genetically sensitive study design on any human behavioral characteristic from political behavior (who is "conservative" and who is "liberal") to obesity to IQ will always show a broad heritability greater than 0 (and always strictly less than 1). Everything that people do is heritable.
The hard answer is that even if a human behavior is shown to be heritable, as all human behaviors are, it still remains unknown how much the behavior is subject to environmental influences. Some human behavioral characteristics with high observed heritabilities are nonetheless highly sensitive to environmental influences. Most human behavioral characteristics are polygenic, that is they are influenced by many genes, each with a small effect, and even monozygotic twins are consistently found to differ in highly heritable characteristics, for environmental reasons that are sometimes still quite poorly understood. Knowing the heritability of a human behavioral characteristic says nothing about how much that characteristic is subject to environmental influences.
Here are the references I promised, recent papers by world-famous behavioral geneticists:
http://people.virginia.edu/~ent3c/papers2/Articles%20for%20O...
http://people.virginia.edu/~ent3c/papers2/Articles%20for%20O...
To sum up, in the context of this thread, a LONG-TERM trend of women having fewer children might be expected to reduce the reproduction most of women who have some genetic propensity to disfavor having children. But all women of all shuffles of the genes respond to societal and individual incentives to have more or fewer children, with few of those incentives yet being well understood. It is certainly possible in principle to reduce the trend toward reduced reproduction, irrespective of which persons (with which genomes) are reproducing.