At 12’ to 14’ distance the spread (assuming “open cylinder” - which is what a sawed off barrel will be), will be about 8-inches in diameter or so. So yes - a lot of .38 caliber rounds going into the perp - but you still need to aim. But easier to aim a short shotgun than a pistol.
And practice. And use buckshot. Birdshot at that distance will just piss the bad guy off unless you can hit him in the head, and maybe blind him.
look at post 47.
Birdshot at 12-14 foot can easily kill you with a body shot.
Really small shot, such as #8 might not, if no vital organs are hit. Heavier shot, like number 4, can penetrate 6 inches.
Here is a whole article on the subject.
http://www.thetruthaboutguns.com/2010/02/robert-farago/shotgun-penetration-with-various-rounds/
I do not think birdshot is an optimum defense load, but it is very dangerous and deadly under 15 feet.