Others who fear they will miss their window have flocked to support groups that have sprung up online.
While demographers acknowledge the Chinese zodiac's cultural importance, some have thrown cold water on the idea that it affects birthrates on a national scale.
Some Chinese provinces and hospitals have at times shown increases in births during lucky animal years and decreases in sheep years, but there is no discernible effect on national demographics, according to Duan Chengrong, a population expert who in 2003 published one of the only studies available on the phenomenon.
"It doesn't mean it isn't a factor," he said by phone last week. "But its effects are likely diluted and overshadowed by others."
Among the factors that have affected China's birthrate in recent decades, and complicated the interpretation of such data, are political and economic upheaval and the government's one-child policy.
In other countries, demographers have also grappled with theories of baby booms linked to specific events.
In the United States, for example, New York newspapers famously announced a boom in pregnancies after the massive blackout of 1965, during which couples supposedly had nothing better to do than procreate. But such a phenomenon was debunked in later years by population experts.
For those in China most schooled in the mystical arts of fortune-telling, all this attention to the Chinese zodiac calendar year is wasted.
"Ordinary people only care about the zodiac because it is much easier to understand than the truth. To us true feng-shui masters, the zodiac doesn't matter at all," said Wen Chaoliang, 39. "What matters most isn't the year you are born but the exact time of delivery."
Feng shui is the ancient art of arranging objects or numbers to improve luck.