You don't get the kind of jokes and puns made among some people who profess to read the Bible a lot.
You get lame jokes like, "Who's the shortest man in the Bible?"
"I don't know."
"Bildad the Shuhite." (Gen. 25:1-2)
It's not claiming dear master Bildad was, actually, the shortest man in the Bible. It's a pun on "Shuhite." "Shoe height," get it? Nothing more should be read into it beyond what you see on the surface.
"May his days be short and another take his office" fits this kind of pattern. The guy wants another to take Obama's office. Not Biden, I'd suspect. You can paraphrase it as "Let his term of office end soon and another take his place" with a Bible-y punny overlay.
As for the text, it's fairly obscure in Psalms--no reason on its own for it to stand out, so I'm not sure run-of-the-mill observant Jews would quickly spot it or place it. It's prominent for Xians because of what Peter said in Acts 1:20 concerning Judas Iscariot, and referencing Psalms: May another take his office. (Now, do you want to read this with the subtext of accusing Obama of betrayal? That's more plausible than trying to incite an assassination attempt.)