1. There is no crisis. Certain conditions produce certain effects. When smallpox is introduced into a population, the population declines, but subsequent generations resist it. The modern world has a perfectly consistent effect on population size, roughly the same as smallpox. The fittest, as always, will survive, and subsequent generations will not have the same problem.
2. The United States is not a "sparkling exception", if you correct your samples. If you reduce Americans to their European subset, you see that Birth rate was 11.6 for Non-Hispanic Whites http://en.wikipedia.org/wiki/Demographics_of_the_United_Stat... ... the lowest of all major groups.
3. The subject of immigration should not come up. Europe will not "save itself" by replacing itself with North Africans. This point warrants no discussion. If you hate Europe as much as the editors of the nytimes, that's another matter, and it's a valid viewpoint to the degree that it is open. It's not open, of course.
4. Europe and Japan are both far too crowded. As long as the situation isn't treated like a crisis, with hopeless policies (mass immigration, mass boondoggles) the long-term effect will be positive.
5. Three big groups who've reversed the trend: Mormons, Albanian muslims, and Ultra-orthodox Jews. A portend of things to come, and it's no surprise that the nytimes is troubled by the situation resolving itself.