If the truth about Obama is ever revealed - that he was an illegitimate president who was ineligible to serve, and that he also engaged in massive vote fraud - then I would hope that Kagan and Sotomayor would be declared illegitimate as well. Toss them off the court.
Even if you could irrefutably prove the premise of your argument, the result you hope for would likely not come about; because, while the President nominates a candidate for consideration to be placed on the SCOTUS, it is the Senate that confirms the candidate to that position.
bump