No. I believe it is the obligation of the several states. Any government that can outlaw abortion, can make it mandatory. (See China's One Chile Policy.)
Oops. Chile=Child
Privileges and immunities clause of the Fourteenth says otherwise. The federal government determines citizenship, not the states. Extent of legal recognition of personhood is one of the primary jurisdictions of the federal government since the 14th was established..
“Any government that can outlaw abortion, can make it mandatory.”
Not so. One, the first amendment protects freedom of conscience. Two, the fourth prohibits unreasonable search and seizure. No such constitutional provisions bar outlawing abortion outright.