It's late and I was hoping to avoid spelling it out, but there is a relevant principle of law called the De Facto Officer Doctrine, which has been recognized by the Supreme Court:
"The de facto officer doctrine confers validity upon acts performed by a person acting under the color of official title even though it is later discovered that the legality of that person's appointment or election to office is deficient. ... "The de facto doctrine springs from the fear of the chaos that would result from multiple and repetitious suits challenging every action taken by every official whose claim to office could be open to question, and seeks to protect the public by insuring the orderly functioning of the government despite technical defects in title to office." - link
Because of this, even if Obama's right to hold office is held to be invalid by the highest court, this will not automatically nullify any laws and executive orders he has signed up to that point or remove any Supreme Court justices he has nominated that were confirmed.
Some of that decision...
While acts of a de facto incumbent of an office lawfully created by law and existing are often held to be binding from reasons of public policy, the acts of a person assuming to fill and perform the duties of an office which does not exist de jure can have no validity whatever in law.
An unconstitutional act is not a law; it confers no rights; it imposes no duties; it affords no protection; it creates no office; it is in legal contemplation as inoperative as though it had never been passed.