When I got home, I looked up the 25th Amendment. It covers Presidential succession. Basically:
Section 1. If the President dies or resigns, the Vice President takes over.
Section 2. If the Vice President's job is vacated, the President gets to nominate a new one, and both Houses of Congress vote on him.
Section 3. If the President says in writing "I can't do this job right now", the Vice President takes over temporarily.
Section 4. If the Vice President and a bunch of other government officers say in writing "The President can't do his job", the Vice President takes over as Acting President.
I've oversimplified, of course, but that's the gist. Now, none of those sections covers the situation where a bunch of citizens think the President is as bad as Hitler, so I was highly confused by the poster. But then I had a thought: Section 4 covers the case of the President being incapacitated; it was almost invoked in 1981 when Reagan was shot. And section 1 covers the case of the President being killed.
Sooo... I'm guessing "Invoke the 25th Amendment" is the crazy right-wing teabaggers' veiled way of suggesting that someone should shoot Obama, thus incapacitating or killing him. What do you think?
(If so, then I am very glad I flipped my middle finger at that lady.)
(And please do not bother pointing out that Bush has also been depicted with a Hitler mustache by protestors. That has nothing to do with why I wrote this post.)