They have to prove that he is unfit. Reasons, reasons, reasons.
But, if they made to claim, he could submit to an exam to prove his mental state. Which would prove to be a mistake because he is a psychopath.
Obama gets a turn to declare otherwise, and then Congress gets a second chance to reconsider. It's up to Obama to prove his fitness, not the Cabinet and Congress to prove his incapacity.
-PJ