The Constitution provides only one way to remove a sitting President: impeachment.
Accordingly, if a court were to determine that he is ineligible for the office, the only recourse would be impeachment.
Recall, however, that a Democrat Senate refused to find Bill Clinton guilty of (blatent) perjury and (obvious) obsgruction of justice.
It would not surprise me if, should Obama be found to have born in Borneo, that a Democrat Senate would not judge that peachy keen.
It's this ignorance that diminishes the BC movement, IMO. Obomba is not going to resign, a radio host isn't going to accomplish anything, and Congress is the most realistic, as well as only procedural, approach to removing him from office, outside of defeating him in 2012.