My mistake.
If by "vast majority" of the 30 million we mean 75% of the 30 million or 22.5 million, this would mean that there was a net natural growth of 7.5 million over 10 years, or 750,000 net new Americans born to Americans each year.
If the death rate were the same - about 0.5% per year, that would mean 1.5 million deaths per year average versus 2.25 new native births, netting out to 750,000.
If we assume that only 90% of the population is native born, that works out to about 44 million native women of childbearing age, of which about 2 million age out every year and 2 million age in every year for a total of 80 million over the period.
So this would imply that only one out of every 20 native born American women of child bearing age have a child in any given year.
Still a number that is very difficult to believe.
According to this, the death rate was .83% per year:
http://en.wikipedia.org/wiki/Demographics_of_the_United_States#Population_growth_rate