I can do a lot better than case. Let us read from the Constitution, which Birthers prattle about a lot, without, apparently, ever having read it.
Art I, Sec 2: The House of Representatives shall chuse their Speaker and other Officers; and shall have the sole Power of Impeachment.
Art.I, Sec 3: The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside.
That is the full story. Congress removes the President from office, and nobody else. Period. Ever. It is 2 + 2 = 4 simple. Has Congress failed in its responsibilities by first certifying BO as President Elect, then not impeaching him, because of (insert your favorite wack-a-doodle Birther theory here)? I don't think so, but even if it has, that doesn't change the Constitution. Congress, and Congress alone, can act on Birther theories. Which means a Birther with any sense will work very hard to elect Republicans to Congress.