First reaction is to say not a chance because TCU needs help by being ranked behind both Texas and Alabama who are playing in the title game. However, if one just goes back to last year Utah was sixth in the final AP poll, but between a beat down over Alabama and a grass roots email effort to the voters Utah was second with 16 first place votes.
The benefit that Utah had was that they beat Alabama who was number one in the country for nearly the entire year before they lost in the SEC title game. However, in saying that TCU is ranked third and really only needs a close game win by Texas over Alabama in the title game. Also, the Sugar Bowl game tonight will have an impact, because Cincinnati is fourth while Florida is fifth and is a very similar game to the Fiesta bowl.
However a win over Florida by an undefeated Cincinnati team will look better in the eyes of some voters because 'hey it's Florida and they are from the SEC' Even with a TCU win over an undefeated and higher ranked Boise State team it is not out of the question of the Bearcats leap frogging TCU (i know a bad pun) for beating the Gators.
TCU will need to have a convincing win over Boise State to try pass the winner of the national title game. TCU may have a tough time blowing out Boise State, because in last year's matchup in the Poinsettia Bowl TCU only won 17-16. Each team has a great offense and a great defense, however TCU's defense has come against some better competition. Also, TCU's rush defense is just amazing which will have a tough time keeping up their average of 80 yards per game when Boise rushes for 195 per game.
One thing to consider but will most likely not be considered is that TCU faced six bowl teams during the regular season and they all have won their games. All four conference foes won: Air Force, BYU, Wyoming, and Utah. Then SMU smoked Nevada and Clemson won their game as well. That should be considered but who knows if the AP voters do their homework when voting -- something I seriously doubt.
To put it simple TCU must win by a large margin, Texas needs to squeak by Alabama in an ugly game, and either a Florida win or a sloppy Cincinnati win. Now, in my opinion TCU will get some first place votes in a similar fashion how Utah did last year, but a split title is just out of reach.