Couldn't this be construed as threatening to assassinate the president?
It's very close IMHO. The chair obviously represents Obama, referencing the Clint Eastwood monologue, and hanging it from a tree represents lynching. If you put a sign in your yard that read "Lynch Obama", I think you might run into some trouble. I would be surprised if the homeowner didn't get the attention of the Secret Service.
I think (and I emphasize "think") that there is a legal difference between saying I will lynch Obama and having subjective "art" that suggests as much. If you had a painting of a crown with a bullet going through it, would it mean you literally wanted to assassinate the queen? I would also submit that my example is far more literal than what is in question here.