Attacking the appointments of a usurper (appointees of Obama; Judges, Cabinet Secretaries, etc ...) based on a violation of the Appointment’s Clause of the U.S. Constitution will not force a Court to consider whether or not Obama should be ordered to vacate the office . It will neutralize Obama in that his appointees will not be able to adjudicate adverse actions against the accused or those who have been ordered to respond to a summons and complaint.
SCOTUS has held a usurper cannot appoint individuals to hold court over the accused if the accused objects to the appointment by the usurper prior to the final ruling. Furthermore, SCOTUS has held the De Facto Officer Doctrine applies if the accused does object to being tried by an appointee of the usurper.
So, if the accused objects to the appointment by a usurper, then a Judge who has not been appointed by a usurper will have to adjudicate the case or the usurper will have to vacate and an eligible President will have to make appointments to replace the appointments by the usurper.
I’m saying that SCOTUS won’t even hear the issue of whether Obama is a legitimate president based on the “political question” doctrine. They’ll just rule, in effect, that the issue of Obama’s qualifications for office were wholly given over to other branches of government and that they therefore lack jurisdiction to even hear the issue of whether or not Obama is a “usurper.” They’ll just throw the case out of court. It’s over.