That policy, in place since Sept. 25, 1980, was tweaked in 2013, permitting a second child if one of the parents in the couple is an only child. The new policy expands that ability to all couples.
Even without any such policy, American women are having fewer children than they did in 1980. In 2014, 2,018 children had ever been born to every 1,000 women aged 40-44 -- or slightly more than two children for every woman. In 1980, the ratio was about three kids for every woman.
The plurality of children born every year are the mother's first. In 2013, 24.7 first children were born to every 1,000 women 15 to 44 years old. The rate of second children was 19.9 per 1,000, with the birth rates of each subsequent position in birth order getting smaller. For every 1,000 women aged 15 to 44 in 2013, there were 0.3 eighth (or higher!) children born. (Think Duggar.)
Since these figures are births per 1,000 women in that age range, we can estimate how many children in each birth position were born each year since 1980.
Now the grim part: Only those first children are allowed. (It's more complicated than this, of course. China's rules allowed for certain exceptions. Since not all children survive to adulthood, Chinese couples were allowed to have a second child if the first died -- but the net number of children that produces is obviously the same.)
If we simply lop off all of the second-or-more children, there would have been nearly 80 million fewer children born between 1980 and 2013.
That's a large, imprecise figure. (In 2014, the Census Bureau estimates that about 148.6 million Americans were aged 0 to 34.) The imprecision comes in many forms. The effect of a one-child policy on how couples decide to have children is impossible to predict, for example. But there's another factor: There would have been fewer women aged 15 to 44 once 1995 rolled around.
If we figure that half of the children that were born because there is no one-child policy were female, the number of women aged 15 to 44 would have dropped dramatically over time.
Which, of course, is a very good reason that the United States would and should not have implemented such a policy. The fertility rate needed to keep the U.S. population from shrinking is 2.1 children per woman. The rate in 2012 was 1.88. (Here's why that figure is different than the first graph.)
A variant of this question would be the reverse: What if China had seen population growth like that of the United States instead of adopting its policy? That calculation would result in some far larger numbers.