No, it does not, but Dead Rising 2: Off the Record has one. The games are basically the same in gameplay. If you must get the normal Dead Rising 2 you should fail the story mission 3-1. You will have all of the areas unlocked and you can free roam until the timer goes off. ( which is at least 4 hours)
Games that I believe have at least a decently long story: Oblivion,Skyrim, Fallout 3, Fallout NV, GTA's, Just Cause 2, Dark Souls, Borderlands, Red Dead Redemption, Little Big Planets, and The Sly Collection (3 games!).
Assassin Creed's can be finished within a decent time.
The longest story i can think of in the list is Oblivion.
The game that I would recommend that most is The Sly Collection.
I think this game is worth buying. I don't find it very glitchy, but I always keep an extra save from my house so if a glitch messes things up. The game is great if Just don't expect to be fighting your way through everything. This game has also a lot of choices in quest and stuff.