If Obama was born in Hawaii, he is a natural born US citizen under jus solis. See United States v. Wong Kim Ark
Nope.
Wong Kim Ark case was bad law in many ways. For one it ignored, abridged, a treaty with the Empire of China that all Chinese subjects shall not be made US citizens or their offspring born inside the United States shall not become US citizens. As you should know, treatise take precedence in the US Constitution as if it was apart of it.
To the point, Wong Kim Ark, Justice Harlen did not call Ark a Natural Born Citizen in the facts of the case or in his holdings. The US Supreme Court in about a half dozen case call all persons native born instead of using the phrase Natural Born to differentiate that their parents were citizens of other countries. The only time the Supreme Court used the phrase 'Natural Born Citizen' when it was clearly that the parents were citizens of the United States and the person in question was born on US soil. see Perkins vs. Elg 1939.
Citizen - not natural born citizen
A senator has to be a citizen to hold office
A vice president or president has to be a natural born citizen. There is a difference.
The Wong case makes her a citizen, not a natural born citizen.
Jus sanguinis and jus solis
Right of blood / right of soil