The best thing for the President and the country, when there is threat of the president being shot - is for the president to hit the ground and then be surrounded by agents.
I can see the president being armed for maybe a last resort, but for the president to stand and return fire - he (or she ) is either going to shoot a Secret Service agent or end getting shot by a Secret Service agent or end up getting shot by the assasin.
My thinking (the last time we had this discussion, before it veered off track) is that this is not far off from the mark.
POTUS travels with a fairly significant group of people tasked to his own personal protection. There's advance groups, scouts, precision marksmen, bodyguards in his immediate vicinity, and a few trucks loaded with stuff that we can only speculate at (but we're probably sure to be impressed by if we ever found out).
Set against that Secret Service entourage, exactly what would the President himself (or herself, in that eventuality), hope to accomplish? Any attacking force sufficient to overwhelm the protective detail isn't going to be stopped by any weapon in POTUS' own hands (and even then, the Prez could just pick up any gun dropped by a now-fallen guard). Furthermore, the President has other things to worry about than scanning for threats; there's no shortage of actual professionals doing that for him. The one threat that everybody understands would be the worst (lone nutcase) is not something that even the President would likely spot first.
I'm a proponent of carry, I carry myself, etc. But if I were in the Oval Office, have to say that I probably just wouldn't mess with it. There's nothing I would be able to do that the detail couldn't.
Even so, I still chuckle at the horror expressed by people over the President carrying a handgun. There's a bunch of people with handguns around him. There's folks with significantly better armament right nearby. Oh, and lest we neglect it, that dude with the briefcase has plans and communications gear sufficient to start the process of burning anyplace on earth to a radioactive cinder, and the President himself has a card with verification codes to begin a nuclear launch. Freaking out over the President having a pocket mousegun when he could wipe places off the map with a phone call is a little silly.