So you have the bizarre spectacle of a young couple cooing over a dog, depopulated villages surrounded by large second homes and condos owned by these young people (presumably for their dog), and newspapers reflecting a growing panic about the future. And as you have said, this is indeed accompanied by a major push for euthanasia. It all goes together so inevitably.
This same scenario is being played out in most of the western world. It's only a matter of time before the US birth rate drops below population replacement.
Actually our total fertility rate has been rising. It is now at replacement rate, 2.1, and will probably continue to rise given the Hispanic birthrate, which is nearing 3.5. And admitting 1.2 million legal immigrants a year plus another 500,000 to 1 million illegal aliens annually will raise our population to close to half a billion by 2060. Our population has increased by 100 million since 1970. Since 2000, we have added 23 million people, approximately the equivalent of the population of the Texas, more than half due to immigration.
100 Million More: Projecting the Impact of Immigration On the U.S. Population, 2007 to 2060
"If immigration continues at current levels, the nation’s population will increase from 304 million today to 468 million in 2060 — a 164 million (55 percent) increase. Immigrants plus their descendents will account for 105 million (63 percent) of the increase. The total projected growth of 167 million is equal to the combined populations of Great Britain, France, and Spain. The 105 million from immigration by itself is equal to 13 additional New York Cities."
So not to worry, the US will retain its status as the third most populous country on earth [behind China and India] for a very long time, i.e., at least through the 21st century when we will be nearing the billion mark.