A day. A week. What happens if this takes years to find out? Is he required to show this before he gets put on the ballot? I am trying to ask the question without asking it if you know what I mean.
If it occurs before the election, he would be immediately disqualified (following the necessarily expedited trip all the way to the SCOTUS). The Democratic National Committee is empowered to name a replacement candidate, which would undoubtedly be Hillary! Clinton.
If he wins the election and this occurs before the inauguration, we'd again have the legal whirl, followed by the election being thrown into the House (which would most likely select Hillary!).
If he wins and is inaugurated, then Obama will be forced out of office (again after the legal stuff) and Joe Biden becomes president in accordance with established rules of succession.
My guess ... if this bears any kind of fruit at all ... is that it would become an issue post-election. Hard to imagine that it would be resolved within the next month.