I don't know that it'll happen at the Elimination Chamber, but I do ultimately see them feuding before it's all said & done. A few months ago, I'd have said something similar to what Messiah said in his post, but that was before I heard & saw the reaction these two factions received during their confrontation on Raw a couple weeks ago.
Fans are digging both groups and they're both a unique faction. Neither faction is a group of loosely aligned wrestlers working towards a common goal or common enemy, there's a much deeper connection that's been hammered into the consciousness of fans since each of them debuted. If The Shield winds up against The Wyatt Family before long, they'll probably wind up being babyface by the time it's all said & done. It wouldn't be the first time a heel has turned face, or vice versa, while in the middle of a feud with someone that's supposed to be on the same "side" as they are.
In some feuds between babyfaces, it's not all that uncommon for a storyline that's centered around friendly competition between two guys who mutually respect each other to change. The storyline goes from that to one in which one face becomes frustrated, feeling he's losing possibly to an inability to ultimately get the best of his opponent. The frustration mounts. The mutual respect gets turned inside out due to anger, friendly competition gets devolved into a bitter hatred and somebody turns heel.
In this case, The Wyatt Family is a creepy, backwoods cult who's only real goal seems to be spreading chaos. It's not one of your more common goals for a heel faction. They don't seem to want to "take over" or establish some "new order" in how things are run like most factions, such as The Shield. For all intents & purposes, Wyatt wants to watch the world burn and be the one who lights the match. The Shield aren't exactly good guys, but they're the lesser of two evils compared to the Family.