“what amounts to recognition of citizenship at conception”
The U.S. Constitution says you are a citizen when you are born.
(from Article II)No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President
(from Amendment 14)All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
True, but it adds, "and subject to the jurisdiction thereof." This is the point people use when saying that we are not required to recognize the children of illegal immigrants (or other foreign nationals) as U.S. citizens, even if they're born on our soil.
Declaring unborn children to be citizens would be a stretch, but declaring them protected by law would not. Animals aren't citizens, but abuse or killing of animals can be punished by law.
And counts your age for purposes of things like voting or military service as starting at birth. Say you're born already 9 months old may be rhetorically justifiable, but there's going to be a lot of legal issues involved in actually codifying that into law.
I'm not saying it shouldn't be done, but I think there needs to be some consideration of the the questions and issues that are going to be involved.