Fertility is one of the best examples of a self correcting problem. Fertility causes populations to contract dramatically faster than most appreciate. The formula for the change between generations is a factor of fertility_rate/2. So if a country has a fertility rate of 1 (which is where many countries are trending, if not already lower than), then each successive generation will be 50% smaller.
A generation is proportional to the the practical fertility window of a given era, so somewhere around 20 years. The deaths (and subsequent population change) will lag behind generations by about 50 years, but become largely unavoidable because female fertility collapses rapidly after ~40. And so when there is a shared fertility rate amongst a population, each ~20 years the population will change by the fertility factor.
So you end up bleeding people fast once the death phase kicks in - you're talking about losing 50% of your population each 20 years. This is why places like Japan will still look to today as the 'good ole days'. They're currently only losing about 11% of their population per 20 years, but with a fertility rate of 1.2 they'll trend towards losing around 40% per 20 years.
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Anyhow, the point of this all is that there simply are not enough people in the world to make up for this sort of loss. And that's if you're willing to accept an adult male with no education and who may not even speak the language, which isn't exactly the foundation of a great society. When you speak of wanting skilled English speakers, both male and female, then yeah - it's really not happening.
So countries will be left to increase their fertility rates or die. Though even that statement kind of misrepresents what happens. Rather the higher fertility subpopulations within society will gradually come to dominate those societies. So in some manner speaking, perhaps the Bible was write and the meek will come to inherit the Earth. An America made of Amish? Pretty funny to imagine, but not really out of domain of possibility at all. Fertility is going to radically reshape the face of Earth and it's difficult to predict what that will look like other than very different.