This concept seems to be a 20th century invention. We know this because Justice Gray mused in the Wong Kim Ark decision that, "neither he nor his parents acting for him ever renounced his allegiance to the United States, or did or committed any act or thing to exclude him [p653] therefrom ..." It makes no sense for a Supreme Court judge to say this if "nothing" under the law could be done by the parents to change the status of their child's citizenship. Also, under the law at the time Obama would have become an Indonesian citizen, nothing prevented him from renouncing his own citizenship as a child.
Aside from this however, the real issue here is if Obama ever acted as an Indonesian citizen as an adult and if the knowledge that he did so and tried to cover it up would affect how people voted for president. Would he still get votes from people if they knew he was an Indonesian citizen and lied about it??
In terms of citizenship, and losing it as a child, I think the pertinent decision is Perkins v Elg:
http://supreme.justia.com/us/307/325/case.html
“Miss Elg was born in Brooklyn, New York, on October 2, 1907. Her parents, who were natives of Sweden, emigrated to the United States sometime prior to 1906, and her father was naturalized here in that year. In 1911, her mother took her to Sweden, where she continued to reside until September 7, 1929. Her father went to Sweden in 1922, and has not since returned to the United States. In November, 1934, he made a statement before an American consul in Sweden that he had voluntarily expatriated himself for the reason that he did not desire to retain the status of an American citizen and wished to preserve his allegiance to Sweden.
In 1928, shortly before Miss Elg became twenty-one years of age, she inquired an American consul in Sweden about returning to the United States and was informed that, if she returned after attaining majority, she should seek an American passport. In 1929, within eight months after attaining majority, she obtained an American passport which was issued on the instructions of the Secretary of State. She then returned to the United States, was admitted as a citizen and has resided in this country ever since.
In April, 1935, Miss Elg was notified by the Department of Labor that she was an alien illegally in the United States, and was threatened with deportation. Proceedings to effect her deportation have been postponed from time to time. In July, 1936, she applied for an American passport, but it was refused by the Secretary of State upon the sole ground that he was without authority to issue it because she was not a citizen of the United States.”
“...Fifth. The cross-petition of Miss Elg, upon which certiorari was granted in No. 455, is addressed to the part of the decree below which dismissed the bill of complaint as against the Secretary of State. The dismissal was upon the ground that the court would not undertake by mandamus to compel the issuance of a passport or control by means of a declaratory judgment the discretion of the Secretary of State. But the Secretary of State, according to the allegation of the bill of complaint, had refused to issue a passport to Miss Elg “solely on the ground that she had lost her native born American citizenship.” The court below, properly recognizing the existence of an actual controversy with the defendants (Aetna Life Ins. Co. v. Haworth, 300 U. S. 227), declared Miss Elg “to be a natural born citizen of the United States,” and we think that the decree should include the Secretary of State as well as the other defendants. The decree in that sense would in no way interfere with the exercise of the Secretary’s discretion with respect to the issue of a passport, but would simply preclude the denial of a passport on the sole ground that Miss Elg had lost her American citizenship.”