How would his Presidency be illegal if his citizenship isn't an issue?
If Obama is foreign born, he is not eligible to be president per the U.S. Constitution.
{ * Minor v. Happersett, 88 U.S. 162 (1874): In this case decided after the adoption of the Fourteenth Amendment, the Court stated (pp. 167–68):
The Constitution does not, in words, say who shall be natural-born citizens. Resort must be had elsewhere to ascertain that. At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first. For the purposes of this case it is not necessary to solve these doubts. It is sufficient for everything we have now to consider that all children born of citizen parents within the jurisdiction are themselves citizens.}