[nonsporting]

This appears to be a "Constitutional" matter and the Supreme Court would have to decide the issue. If Obama is found not to be qualified, even after he is elected, the Chief Justice could refuse to swear him in (the "Constitutional" thing to do). He cannot be seated as President unless and until he's sworn in. (Correct?)

Who is then next in line for the Presidency? We go back to the Electors who would then choose a qualified candidate?

Would Roberts keep his oath, even in the face of possible impeachment?

[Pilsner]

the Chief Justice could refuse to swear him in

The Chief Justice administering the oath is traditional, not required. Calvin Coolidge was sworn in by a Notary Public.

[21stCenturyFreeThinker]

Who is then next in line for the Presidency? We go back to the Electors who would then choose a qualified candidate?

If it is clear that he isn't qualified before the Electoral College votes then they could just vote for another candidate. Any candidate they like. Even Al Sharpton. Electors are not Constitutionally bound to vote for any specific candidate even in a normal case. See this article about faithless electors

If it happens after the Electoral College votes then the Vice President elect will become acting President until another candidates qualifies. The problem is that there is no way specified for a candidate to qualify at that point.

If it happens after he's inaugurated then he has to be impeached and convicted by Congress.

Bottom line, I really doubt anybody will push it after election day.