If it were merely an issue of citizenship, why would the founders have bothered to write a specific requirement differing from that used for Senators, Congressmen, and judges to the SCOTUS?
The Tribe/Olson 'Natural Born Citizen' Memo
The Constitution does not define the meaning of “natural born Citizen.” The U.S. Supreme Court gives meaning to terms that are not expressly defined in the Constitution by looking to the context in which those terms are used; to statutes enacted by the First Congress, Marsh v. Chambers, 463 U.S. 783, 790-91 (1983); and to the common law at the time of the Founding. United Suites v. Wong Kim Ark, 169 U.S. 649, 655 (1898). These sources all confirm that the phrase “natural born” includes both birth abroad to parents who were citizens, and birth within a nation’s territory and allegiance. Thus, regardless of the sovereign status of the Panama Canal Zone at the time of Senator McCain’s birth, he is a “natural born” citizen because he was born to parents who were U.S. citizens.
and
Indeed, the statute that the First Congress enacted on this subject not only established that such children are U.S. citizens, but also expressly referred to them as “natural born citizens.” Act of Mar. 26, 1790, ch. 3, § 1, 1 Stat. 103, 104.
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Historical practice confirms that birth on soil that is under the sovereignty of the United States, but not within a State, satisfies the Natural Born Citizen Clause. For example, Vice President Charles Curtis was born in the territory of Kansas on January 25, 1860 — one year before Kansas became a State. Because the Twelfth Amendment requires that Vice Presidents possess the same qualifications as Presidents, the service of Vice President Curtis verifies that the phrase “natural born Citizen” includes birth outside of any State but within U.S. territory. Similarly, Senator Barry Goldwater was born in Arizona before its statehood, yet attained the Republican Party’s presidential nomination in 1964. And Senator Barack Obama was born in Hawaii on August 4, 1961 — not long after its admission to the Union on August 21, 1959. We find it inconceivable that Senator Obama would have been ineligible for the Presidency had he been born two years earlier.
Regardless of what one thinks of Tribe and Olson, both are recognized Constitutional scholars and both have been listed at one time or another as possible SCOTUS justices. Note that they interpret the Constitution and related cases to mean that natural born citizenship includes birthright citizenship (jus solis) and by blood, (jus sanguinis.)
We need to take this to SCOTUS and get a ruling. By 2050, one in five residents of this country will be foreign born. Today, one in 8 is foreign born, the highest it has been in 80 years. We have 300,000 to 400,000 anchor babies born each year. The definition of natural born citizenship is not settled law. It must be resolved sooner rather than later.