This is very sad. Unfortunately, this will keep happening until ISIS is stopped.
Or, when obama is no longer president.
This seems more like a protracted hostage situation, with 'no more air strikes' being the demand that if not fulfilled, leads to another dead hostage. This framing of the situation does target the president directly, but not because he is Obama: the president is the only person who can 'stop' the next murder.
There really is only one way any president should respond to this. In public anyway.
Oh, I believe that the airstrikes shouldn't be stopped. I think obama actually should bomb more, because if he doesn't, ISIS is going to grow, and more journalists beheaded.