In Burton v. United States:
the Supreme Court ruled that a provision of federal law which on its face purported to make one convicted of bribery
ineligible to be a United States Senator, could not act as a forfeiture of a Senators office, since the only way to remove a Member under the Constitution was by the
Senate exercising its authority over its own Members.
RELEVANT CASE: AN INELIGIBLE SENATOR COULD NOT BE REMOVED (EXCEPT BY THE SENATE).
http://74.6.239.67/search/cache?ei=UTF-8&p=Congress+removal+from+office&fr=yfp-t-501&u=lugar.senate.gov/services/pdf_crs/Recall_of_Legislators_and_the_Removal_of_Members_of_Congress_from_Office.pdf&w=congress+removal+remove+removed+office&d=TA4d1t29TdK9&icp=1&.intl=us&sig=VLhFTADt5rS1TVD7Vsyp9g—
I see your perspective, but tell me, which President is going to remove the one in the Oval Office heading the executive branch. ... What are you digging for, anyway?
The case is not relevent, BTW, because it does not question eligibility to run and hold the office elected to. But that was a nice try.
The Constitution most explicitly makes someone not a natural born citizen not eligible to the office of President.
Totally different situation. Impeachment is for President's who misbehave, not for ineligible usurpers.