Two Presidents before Obama, not counting those who were citizens at the time of the adoption of the Constitution, had a parent who was not born in the US—Chester Arthur (whose father was born in Northern Ireland) and Woodrow Wilson (whose mother was born in Carlisle, England). I don’t know if Arthur’s father or Wilson’s mother were formally naturalized. Wilson’s mother lived in the US from the age of 4. Arthur’s father lived in Quebec before coming to the US, and some people claimed that Chester Arthur was actually born across the border in Canada rather than in northern Vermont.
As for Woodrow Wilson, his mother became a "citizen" when she married her husband who was a citizen, by way of a Congressional Act of February 1855, which stated,
any woman who might lawfully be naturalized under existing laws, married, or shall be married to a citizen of the United States, shall be deemed and taken to be a citizen. [Act of February 10, 1855, 10 Stat. 604, section 2]
This act was enacted in 1855. Woodrow Wilson was born in December 1856. Therefore, Wilson would have been born to two citizen parents...on U.S. soil and therefore an NBC.
Well sh!t, that settles it, bammie is legit!
Wilson's mother would have become a citizen upon marrying his father, assuming she was not naturalized by derivation when her parents were naturalized.
Arthur's father was naturalized, but not at the time of Chester's birth. Rather when Chester was 14.