As it is, many of the most intelligent Westerners are limiting their child-bearing in large part because of the huge tax burden imposed on them by governments which force them to pay for raising the many children produced by less intelligent Westerners.
While there is some truth to this, I think feminism (career over family) and materialism (having the best stuff trumps everything) is as much or more to blame. The flip side of the coin is that the Arab hordes are sure making use of their extras to fuel their Jihad (intentionally or not). The West has to deal with that somehow--so far. we've been doing it poorly. Our politicians (egged on by economists) are obsessed by getting the immigrants in so we can make up for our dearth of children. They seem not to care that we are importing lots of Muslims as well--and the ultimate impact that will have.
Men have been doing the "career over family" act for a long, long time, and women finally figured out why. Don't look for that trend to reverse. But it usually results in a choice for late child-bearing, rather than no child-bearing. Medical technology has already gone a long way toward eliminating the biological obstacles to having as many children as are wanted, at any age, and progress is continuing fast.
The bigger problem is socialism, which is raiding the resources of the productive class to support the offspring of the non-productive class. Socialism is also at the root of the illegal immigration problem -- not only because of all the federally mandated perks of illegal immigration (free schooling for the ids, free emergency medical care, etc.), but because illegal immigration is needed in order to prop up socialism, which is in turn needed by politicians who use government hand-outs to buy votes.
Dump the socialist policies of minimum wages, tax code coercion or (in some states) outright requirements for employers to provide medical insurance, housing codes which mandate middle class living standards for the poor (thus driving up the price of housing, and pushing more people into the position of not being able to make ends meet), liberal unemployment benefits, and federally funded financial aid for college and job training programs, and suddenly the "need" for all these illegal workers will vanish, as citizens march into all those jobs because their free ride has ended and employers can hire them legally for what they're really worth.