Edit: As far as I can tell, it's a Winchester M1887, 12g lever action shotgun, or some modern remake (not sure if there are any 12g modern repros, 10g is more common.) Sawed-off in the movie, of course.
Yes, sadly, a original black powder 1887 was hacked for the movie. The 87s were problematic. They were black powder era 12 bore shotguns. They weren't too sturdy for military/defensive roles. They worked OK for hunting. The 10 bore was the 1901. There have been some attempts that failed to clone these shotguns by Tri-Star from Australia. Norinco did clone them in metric. They are banned for a few more years though. The problem was being outmoded when they were introduced. That was the same fate of the Winchester 1893 pump shotguns. Nitro smokeless was coming into common use. Damascus steel wound and welded barrels were becoming obsolete. Nitro proofed steel tubular barrels were more durable and the latest fad. That fad has lasted quite a time.
The one in the movie was a complete fake that did not fire. The flames and such were edited in after for effect. It was all aluminum with balsa wood stocks. It only weighed 2 pounds or soo which is why he could just flip it around one haned and work the action.