Here are the relevant parts of the Constitution
4A
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated …
This was part of the basis of
Roe v Wade: right of privacy derives from "secure in their persons".
5A
No person shall … be deprived of life, liberty, or property, without due process of law …
14A
… No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law …
These two say that the state must jump through hoops before it can properly kill you (unless, that is, some random police officer gets scared and decides you need to be less alive).
No other part of the Constitution makes any mention whatsoever about killing, either by the state or by a citizen. The Constitution literally does not prohibit murder, theft, depravity, coarse language nor a host of other things that are or have been recognized as unacceptable behavior.
There is no Right-to-Life in the Constitution. Hence, abortion cannot be considered wrong under the Constitution because it says nothing about whether private citizens are expected to respect any other's right to live, be they human, feline, vermiform or microbial.
And yet, by the same token, no one is granted any right to life-saving actions or treatments. Citizens are not required to aid each other (this in fact might be seen as something of a flaw in the intent of the document), so if the law tells them not to help, that law is not outside the bounds of the Constitution, and finding a premise upon which a doctor should break the law to save someone's life becomes profoundly difficult.