Once you reach this point in the season and your team is not ranked in the top six, you can assume that they won't be reaching the BCS National Championship (unless it's 2007), and all the focus switches to conference championships and at-large BCS berths.
For the Arkansas Razorbacks, you'd think sitting at No. 7 in the most recent BCS standings would put them in prime position for an at-large come December. But there are still a few major obstacles they would have to overcome to reach a BCS bowl.
The biggest problem is the limit on the number of teams from any one conference that can play in BCS Bowls (a rule that only ever affects the SEC). The only way three teams from the same conference can play in BCS games is if two happen to finish ranked in the overall top two in the final BCS Standings without winning the conference championship (which I can't imagine ever happening).
Right now, the LSU Tigers and Alabama Crimson Tide would claim the SEC's two spots, even after Saturday's game. The loser won't drop out of the top six, barring an absolute blowout.
Saturday's game between Arkansas and the South Carolina Gamecocks is a BCS at-large elimination game. The loser has no chance of getting an at-large bid (South Carolina, being in the East division, could still play in and win the SEC championship).
Unfortunately, while a loss could effectively end the loser's hopes, Arkansas doesn't get much of a boost with a win. If they win and Alabama loses, I have to imagine the Crimson Tide will stay ahead in the rankings, considering Alabama clobbered Arkansas 38-14. And if LSU loses, it all still comes down to the regular season finale between the Tigers and Razorbacks.
Arkansas' Best Chance
I would say the Razorbacks' only chance of earning an at-large bid is winning out, which would include a win in Baton Rouge on November 25. If they win at LSU, they will certainly pass the Tigers in the rankings, and an at-large would be all but locked up.
Rankings-wise, Arkansas is already in a position to secure a BCS bid. But they have to overcome the BCS conference limit, and the only way to do that is beat LSU.
There are other scenarios that would get Arkansas an at-large bid. Alabama could of course lose another game after the hypothetical loss to LSU. But the way the Crimson Tide are playing, I don't see that happening.
LSU could also have a similar breakdown, but even if they did, the Razorbacks would still have to beat them head-to-head (or risk falling behind too many potential at-large candidates like the Oklahoma-Oklahoma State, Oregon-Stanford and Virginia Tech-Clemson losers).
There is also the possibility of LSU beating Alabama and losing to Arkansas, which would create a three-way tie in the West, with the highest ranked team going to the SEC Championship. But these scenarios are all speculative at best. For Arkansas, the SEC's second BCS berth will be earned on the field in Baton Rouge in the regular season finale.
That is, of course, if the Razorbacks can get past the South Carolina Gamecocks today.