The Supreme Court ruled in Fairchild v. Hughes that all citizens have a right to a government that is administered according to law. The seating of an ineligible president does not conform to the law (or the Constitution), thus such a person is not technically a "sitting" president. Under Art. III, it is within the judicial power to resolve controversies that arise under the Constitution. This is not a power delegated to Congress. There's no reason that the courts cannot enforce Art. II and the 20th Amendment in order to ensure that all citizens have a government that is run according to law.
I would like to see/know some means or indisputable mechanism given by the Constitution as the ‘supreme’ means by which Obama could be removed from the office of POTUSA. I am wondering why the Founders used the word ‘under’ in Article III Section2 when addressing the power of the SC instead of a common word such as ‘concerning’. I can take such wording to have meaning that the Constitution is ‘over’ the SC and that takes me to the Preamble that says upfront ‘We The People of the United States in order to form a more perfect union........ do ordain and establish this Constitution for the United States of America.’. Looking at it this way it seems Congress has to take an issue with POTUSA to the people. I think Obama and his enablers recognized a convoluted action would be necessary to remove him.
Neither the 9th US Circuit Court of Appeals nor the Supreme Court of the United States saw fit to overturn Judge Carter.
Neither the legislative branch nor the judicial branch have found that an ineligible person was inaugurated.
Courts have ruled that Obama qualifies as a natural born citizen. No court has ruled to the contrary.
For example, one of several rulings: Rhodes v MacDonald, US District Court Judge Clay D. Land: A spurious claim questioning the presidents constitutional legitimacy may be protected by the First Amendment, but a Courts placement of its imprimatur upon a claim that is so lacking in factual support that it is frivolous would undoubtedly disserve the public interest.US District Court for the Middle District of Georgia, September 16, 2009.
http://www.scribd.com/doc/19809978/RHODES-v-MacDONALD-13-ORDER-denying-3-Motion-for-TRO-granting-8-Motion-to-Dismiss-Ordered-by-Judge-Clay-D-Land-on-09162009-CGC-Entered-0