It certainly won't be Bielema. That dude's buyout clause is obscene.
This is a great question though. I think Gus is given at least 4 years and I think he'll have AU winning 8+ by year 2. Mark Stoops is in a job with limited expectations. He gets a big bonus for winning TWO sec games. He could stay there for 4-5 years before they start to worry (though if he's successful he might bolt).
I'm gonna go with Butch Jones as being most likely to get fired first, but even then it's a long shot that he'll get fired. He's a decent coach. He has them at 7 wins next year.
1. Gus Malzahn (Auburn's impatient and Malzahn can't coach a defense. 2-3 years) 2. Butch Jones (This hire could get really bad really fast. 2-3 years) 3. Mark Stoops (I don't see him finding success here, but that has less to do with coaching and more to do with the fact that he's at Kentucky. Kentucky will be patient with him so I give him 4-5 years) 4. Bret Bielema (This is a great hire for Arkansas. It's so great a hire that I can't understand why in the hell Bielema would take this job. As long as he can recruit, and I think he can, he should be able to compete for the SEC West and be routinely in the top 3 in the division. 5+ years)