So you'd be fine with some foreigner coming the US, say as an adult, possibly as an agent of his government, falsefying his identity, pretending to be a natural born citizen, and winning an election for President, or even some lessor office for which one must at least be a citizen. Then after all that was disovered continuing to exercise the powers that office?
I wouldn't.
For all we know that has already happened. I'm not fine with Obama being president. But he is. And the only constitutional provision for removing him from office is the impeachment process.
Do you think in such a case that a ruling by the Supreme Court that he was not "eligible" is going to accomplish anything? Who is going to enforce it? And on what Constitutional authority can the Supreme court remove him from office?
I wouldn't.
How far are you willing to go?