That's not an easy question. America is increasingly a country of men and not a country of laws.
I don't know if Obama desires this drift, or is simply enjoying the benefits of it. Countries of men don't have formal mechanisms to remove bad leaders. They'll leave when their term is up, because they fear the wrath of other men, not because they fear the law.
Beyond that, I don't know what to tell you, other than to suggest you read up on how the Romans fared with issues of succession and removing corrupt leaders. This isn't the country you grew up in, but its change is nothing new. This path has been walked before by the republics of old.
A sitting President, which despite the illegality, is what Obama is, can be removed only by:
(1)Impeachment in the House and Conviction in the Senate.
(2)Resignation
(3)A congressional finding of incompetence to exercise the office
(4)Death
MHG has long felt that by the original ineligibility, Obama is actually not the President. Since he occupies the office and exercises the powers, that is a moot point. Furthermore, there is nowhere to bring that point for consideration.