If Obama was never eligible, he never lawfully occupied the office. So, the procedure would to remove him would be the same as removing an someone pretending to be the POTUS. Federal Marshals drag him out by the ear.
There is plenty of legal precedent for this position.
The open question would be if Biden is legally the VP, and therefore the successor POTUS.
Kind of a difficult argument to press forward based on the fact that the only way to remove a sitting President is through impeachment.
He candidacy was approved by 50 secretaries of state, he won the electoral, Congress certified the election, and the Supreme Court Justice of the United States swore him in.
He is addressed as Mr. Present, he resides at 1600 Pennsylvania avenue, He signs bills that have become law, and he’s vetoed bills, and all this with with nary a word from Congress on his “Presidential Stature”.
Go ahead, take your case to court and prove he is not President. I’ll wait until you prove me wrong.
You left out two steps. A federal judge would have to issue an arrest warrant before the Marshals Service could enforce it. And a U.S. Attorney or the Justice Department would have to file a criminal complaint before a judge would issue an arrest warrant.
Obama would claim his right to the office under the Supreme Court’s “de facto officer doctrine:” 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. Norton v. Shelby County, 118 U.S. 425, 440 (1886). “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.”
In non-legalize, because the Congress (certifying his electoral votes, sending him bills to sign, confirming his nominees) and the Supreme Court (ruling on the constitutionality of his policies) have interacted with Obama as if he were the legitimate President, they have forfeited the legal right to challenge his legitimacy.