I think at least three things need to happen:
1) Down year for traditional powers and/or fortunate scheduling
2) Outstanding player or two at a OB and/or RB with a coach smart enough to use them properly or at least get out of the way
3) Luck in the form of very limited injuries and events falling in just the right way during game play -- this is usually necessary for even the best teams to win it all, but especially so for a team like the barn, or the Mississippi schools.
Every few years, there comes a perfect storm in which the traditional powers are slightly down or lose a game they shouldn't, while a medicore team with an truly exceptional skill player at QB or RB and/or a decent coach gets just the right amount of breaks to give themselves a chance. Examples of teams who won national titles this way in relatively recent decades include Pitt, Georgia, Georgia Tech, BYU, barn, Tennessee, and Colorado. It's particulary tough in the SEC for this to happen, but it can. If Newton had ended up at Mississippi State under Mullen, I think they could have had the barn's season. If TAMU had not been forced to cancel their first game this season, they probably beat Florida and even with an LSU loss, might be #2 in the country right now. Of couse, the Aggies have some pro-level talent in the trenches and an offensive scheme that caught teams off guard this season. This is an example of the luck factor. If there was not a hurricane to cancel TAMU's first game, things might be very different in the SEC West right now. Next year, Manziel is not a surprise and they will have lost some really important players from their lines. Will they be a Tebow-era Florida team for a couple of years? We'll see.
Aside from schools like Vandy (where academic standards are a tremendous recruiting handicap) or Kentucky (where football is only a diversion until basketball sesaon arrives), any team in the SEC could make a run, especially with a playoff system. Almost all other schools in our conference have SEC-level talent at the starting level. It just takes the right circumstances for those teams to have their shot at the end of the year. Fate is fickle and some doormat teams never get a chance.