CS, I took your idea and decided to check if these numbers were at all realistic. I went to the CIA World Factbook for my data, so this is definitely NOT Wikipedia data. Here are the total fertility rate numbers for eight European Countries and eight primarily Muslim countries as well as the United States:

Total Fertility Rate – Children born/woman

Russia 1.41
Italy 1.31
Germany 1.41
United Kingdom 1.66
France 1.98
Spain 1.31
Poland 1.28
The Netherlands 1.66

Iraq 3.86
Iran 1.71
Saudi Arabia 3.83
Egypt 2.66
Pakistan 3.6
Libya 3.08
Turkey 2.21
Afghanistan 6.53

United States 2.05

No European country has a fertility rate that will support its population, France is the closest; however it should be noted that while muslims make up less that 10% of the total population, approximate 30% of the under 18 years of age is Muslim. This may account for the comparatively high fertility rate in France.

The only primarily Muslim nation that has a fertility rate that will not support its current population is Iran. The rest range from moderate to explosive growth rates. The United States has a fertility rate that would come close to supporting our present population, however this country will continue to grow so long as immigration is left unchecked.

The facts do appear to support the video as does the well researched book, America Alone.