There is an obvious fallacy in describing the failure to demand proof of eligibility from Mr Soetoro Soebarkah as “the will of the people”: that would mean that every so-called “representative” body has the right to ignore any Constitutional provision, because that, allegedly, is “the will of the people”.
And of course, in a literal sense, it isn’t and cannot be. “The people” never choose to have an unconstitutional “President”.
That fallacy, and the interpretation of the law which it implies, has apparently been refuted by Marbury vs. Madison.
It does lead to the possibility of usurpation of legislative power by the judiciary, but in this case, demanding documentary proof of birth circumsnances, or even reaffirming a long-established tradition in the definition of a “natural-born citizen”, is no such usurpation.