A person not eligible cannot be a President, let alone a sitting one. Not eligible means not President.
Exactly what is driving the country nuts, Gato!
Here's the problem in a nutshell. "Not eligible" DOES NOT MEAN "not President." It means he is holding the office, but not legally. That is he is the sitting POTUS de facto and just perhaps, since no court has yet ruled on it, not POTUS de jure.
The history of Western Civilization is replete with illegal Popes, Kings, Bishops, etc. In many cases with two or three characters competing against each other as claimants, each making rules and laws, and maintaining a government, all the while condemning each other!
In effect, by voting for him in The Electoral College, and by allowing BHO, Jr. to take the oath of office, Congress in effect, altered the Constitution and granted BHO, Jr. a "waiver."
Now, only Congress can undo that. The Constitution Obama wrecked, now protects Obama. Obama can be removed by Impeachment and Conviction, Resignation, or under a very narrow and strict set of circumstances, be declared incompetent to discharge the duties of the office.
In reality, Gato, this is our de facto POTUS until 2012, and unless some state legislatures and governors stop pussy-footing about, perhaps longer. Right now, all they are doing is helping Obama set up a trap play with all this Birth Certificate nonsense.
Team Obama wants to change the dictionary. They have invested in a huge and apparently successful campaign to convince people who should know better, namely our elected representatives,
So far, to the best of my knowledge, not one (1) elected Republican has even mentioned, "Natural Born," as the key eligibility factor of Article II, Section 1. There is an increasing constitutional scale of eligibility for each federal elective office in the Constitution, culminating in the requirement for the President to be a "Natural Born," citizen.
It does not require an intimate knowledge of Vattel, or Rocket Surgery to figure it out in context. Obama ain't eligible.... but he now holds the office, having been given it by The Electoral College, and being sworn in by the Chief Justice. The Representative branch, the Judicial Branch, and the Executive branch colluded, and it is done.