This is a great question. Zero population growth (ZPG) is when the population neither grows nor declines. So, to fall below the zero growth population is in essence to decrease in population.
Now as to whether the United States and other developed nations can fall below the ZPG point, the answer is clearly a resounding yes.
Scholar state that each woman needs to bear approximately 2.1 children to keep the ZPG. So, if the women of a nation do not keep the 2.1 birthrate, that nation will eventually decrease in population. We can see this in nations like, Japan. Since 1975, Japan has fallen below the 2.0 birth rate. Italy is also following suit. This means that these nations (advanced nations) in the future will decrease in number.
With this said, immigration might change things, but this is to introduce another factor.