Cruz's father is a Cuban defector who became a naturalized US citizen in 2005.
So, I guess the mom was enough. Just checked, and Obama's mom was born in Kansas, so that entire birther fiasco was a moot point.
From Wiki:
The weight of legal and historical authority indicates that the term "natural born" citizen would mean a person who is entitled to U.S. citizenship "by birth" or "at birth," either by being born "in" the United States and under its jurisdiction, even those born to alien parents; by being born abroad to U.S. citizen-parents; or by being born in other situations meeting legal requirements for U.S. citizenship "at birth."
The precedent seems to go all the way back to Chester A. Arthur, the 21st president, born in Candada to a US mother and Canadian father.
Apparently Obama should have just told everyone he was born on Mars to a US mother. It wouldn't have mattered by rule of law.