Obama's case is a bit different than Marie's situation since her parents were doubtlessly US citizens at the time of her birth in the US. Also, citizenship law had changed significantly and had been radically reinterpreted by the courts in the years from 1930-1970. In fact, laws were changed to the point of making it difficult to even determine what an NBC was. The courts and Congress allowed dual citizenship, and marriages of mixed citizenship to be possible, which is something that the Constitution had never conceived of. These things made it difficult to know which parent was the controlling factor in inheriting Natural born US citizenship. In Obama's case one parent was not eligible to pass on US citizenship outside of the US, while the other was not a US citizen at all.
Before the Civil War and when the Constitution was written, a person became a citzen in only 2 ways A)by blood to US citizen parents or B)by naturalization. The 14th amendment changed that by adding a vague definition of Ius Soli which now adds the possibility of obtaining US citizenship by place of birth rather than by blood. The problem is that inheriting US citizenship by blood is clearly NBC but obtaining it by place of birth is not defined as NBC in the 14th amendment. Wong Kim Ark tried to deal with this question. It established that Wong was a US citizen, but not whether he was an NBC.
The Naturalization Act of 1855.
"In 1855 allowed alien women to acquire citizenship by marrying a United States citizen, or upon his naturalization. A woman’s citizenship was directly tied to that of her husband. Women and children automatically received naturalization upon the husband or father’s naturalization. "