The prevailing Constitutional requirement for president is to be a natural born citizen, not just a U.S. citizen, and especially not by simply being “born or naturalized.” It’s why the SCOTUS said the 14th amendment does NOT say who shall be natural-born citizens. There’s a material difference between these classes of citizens. Obama is not and cannot be eligible.
The Constitution describes only three types of US citizen. Currently one is either natural born or naturalized. There is no fourth category. Only naturalized citizens are barred from the Presidency.