First, a couple of pertinent facts regarding child birth and society:
- The fertility rate in the US is estimated at 2.05 births per woman in 2009.
- With some variance, the replacement fertility rate is around 2.1 births per woman.
Even applying the utilitarian ethos implied in the OP, the question seeks to address a problem that, in the United States, does not exist. Absent immigration, US population would be largely stable or perhaps even trending downward; at best the US population is maintaining its numbers. Even if resource management were at issue (something for which the case has not been made), curtailing immigration would be the immediate palliative, for regulating birth rates would require several generations for the impact on the larger population to appear, due to the phenomenon of population momentum. Regulating child bearing is the wrong solution to a nonexistent problem; lacking justification, its imposition would be lacking in justice.
Within the question's own ethos, the answer is already and emphatically "no".
Moreover, the United States is not a nation driven by utilitarian ethics. Our government exists to "
secure the Blessings of Liberty to ourselves and our Posterity." Our rights are the rights of individuals. "Liberty", within the framework of the Constitution, is not championed as a monolithic society doing what is best for itself, but is rather an endorsement and protection of each individual man's capacity to determine what is best for himself, with the larger society being so ordered as to give each man maximum latitude in that determination. This principle is explicitly stated in the Preamble of the Constitution, and its influence shows in every Amendment in the Bill of Rights, appearing again in explicit form in the
10th Amendment:
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
As a point of philosophy, one can debate
ad infinitum the wisdom of a particular woman or couple having a child. However, wise or unwise, that choice is for the individual woman or couple to make; government is explicitly denied a capacity to govern over that choice. Liberty in this country includes the capacity to make mistakes, to do that which is unwise; we are a free people only because we are free to err, and free to suffer the consequences of our error.
Thus one may safely say that, not only should the question be answered with a passionate "No!", the question itself is repugnant--and should be repugnant--to a free people whose defining civic virtue is that of liberty of the individual. Child bearing is a blessing, a gift from God to each woman, and no one on earth should presume to interfere.