If everything goes right, I think the Cubs could be competative by as soon as 2016.
I don't see any reason to give up on 2015.
The bullpen should be in good shape, and there are plenty more promising relievers coming out of the system as reinforcements.
The infield is a weakness right now, but the Cubs graduate no fewer than five infielder who project as potential major league regulars this season or next (Baez, Bryant, Villanueva, Olt, Alcantara). If just two of them stick and Rizzo and Castro bounce back, the infield doesn't look bad at all. I can make a case that the Cubs could have the best infield in the NL by September of this season.
Catcher looks good. Depth is an issue, but I think Castillo/Kotaras could backstop for a winning team.
Outfield is a bigger problem. If some of the infielders spill into the outfield, that would help. If Vitters can claim left field, that would really help. Other than that, until Almora/Soler arrive (if they do) the Cubs are looking at an assortment of wild cards out there. I'd be happy to see a Triple A or young major league outfielder show up in a trade this season.
Starting pitching - this one is more iffy. I suspect the Cubs can fill out the back half of a rotation fairly well, but they'll need an arm or two in the front to compete by 2015. The bullpen could be good enough, though, that they can get by with a more average rotation and still make a run at the wild card. I'll admit this is the trickiest part of the puzzle. Signing Masteron, Scherzer, and Shields would turn it around in a hurry, but landing all three is unlikely. Landing any of them, as with any free agent, isn't a guarantee.
I know I'm just going to be dismissed as an unobjective, irrational, kool-aid drinking front office apologist by the majority of the fan base for saying it,but I still see no reason to write off 2015. They may not win the division, but I expect them to at worst be fighting for a wild card.