GLENDALE, Ariz. -- Ohio State and Texas both had dreams of playing for a BCS National Championship this season.
The Longhorns were ranked No. 1 in the country for three weeks this season, until losing at Texas Tech 39-33 on Michael Crabtree's winning touchdown catch with one second to play Nov. 1 at Jones AT&T Stadium in Lubbock, Texas.
Even after that loss, Texas believed it still deserved to play for the Big 12 championship because of its 45-35 victory over Big 12 South foe Oklahoma in the Red River Rivalry in Dallas on Oct. 11.
Instead, the Sooners won the Big 12 South's complicated tiebreaker over Texas and Texas Tech, and then blasted Missouri 62-21 in the Big 12 championship game in Kansas City on Dec. 6.
The No. 1 Sooners will play No. 2 Florida for the BCS National Championship on Thursday night in Miami.
The No. 3 Longhorns are still hoping for a split national championship. They'll probably have to beat No. 10 Ohio State soundly in Monday night's Tostitos Fiesta Bowl at University of Phoenix Stadium to have any chance. Even then, Texas' chances of finishing No. 1 in the final Associated Press Top 25 poll seem slim at best.
"I think we definitely have a chance," Texas receiver Jordan Shipley said. "Obviously, we lost one game to the No. 5 team in the country in the final seconds of the game. We feel like we have a chance to get some first-place votes if we come out and play well against a team with the tradition that Ohio State has."
The Buckeyes have had their eyes on the BCS title game since losing to LSU 38-24 in the 2008 BCS Championship Game in New Orleans. It was Ohio State's second straight lopsided loss in a BCS title game. The Buckeyes lost to Florida 41-14 in the 2007 BCS title game on the same field where they'll play Monday night.
The Buckeyes were so determined to get a third chance at winning a national title that highly regarded juniors such as linebacker James Laurinaitis and cornerback Malcolm Jenkins returned to Ohio State for their senior seasons.
With 19 starters returning to a team that went a combined 33-5 the previous three seasons, Ohio State was a popular choice during the preseason to return to the BCS title game. The Buckeyes were ranked No. 2 in the preseason Associated Press poll.
Instead, Ohio State's dreams were dashed in an ugly 35-3 loss at Southern California on Sept. 13. The Buckeyes recovered to win eight of their past nine games, losing to Penn State 13-6 on Oct. 25.
Even though Ohio State fell short of its lofty goals this season, the Buckeyes maintain they still have plenty to play for against Texas.
More than anything else, the Buckeyes want to prove they're better than their past two performances in BCS bowl games.
"Really, the careers of this senior class will be determined by this bowl game," Laurinaitis said. "A lot of people would see that as a lot of pressure, but we're excited to play."
Laurinaitis said the Buckeyes might be more prepared to play because they're not under such a big microscope. The past two seasons, Ohio State seemed to wilt under the pressure of playing for a national championship.
"It would be nice to win this big game," Laurinaitis said. "We know we can win these games. It's nothing psychological. It was just a matter of us not executing in the past. I think we're a lot more relaxed this time and guys are focused."
Even though the Longhorns aren't playing for college football's biggest prize, Texas quarterback Colt McCoy insists his team will be ready to play the Buckeyes.
With a victory over Ohio State, Texas can win 12 games in a season for the first time since 2005, when quarterback Vince Young led the Longhorns to a 13-0 record and their first national championship since 1970.
McCoy said the Longhorns have to play well against Ohio State, and then let the polls sort themselves out.
"We're not focused on any of that," McCoy said. "We have to go out and play our best game of the season. You can let the voters sort it out the way they want and let the voters decide which team is No. 1. Ohio State is a great football team. We know they're going to play a great game."
The legacy of Ohio State's senior class -- and the reputation of the Big Ten Conference -- might be riding on it.
Big Ten teams are 1-5 in bowl games this season. Its teams have lost five consecutive BCS bowl games by an average of 20 points.
"You really can't argue because the Big Ten hasn't played well in bowl games," Jenkins said. "But that really has nothing to do with what we have to do. A win would be a sight for sore eyes for our fans and for us. We haven't been satisfied with how we played in the last two bowl games. We have to change that."
If not, the Buckeyes will be remembered as a team loaded with talented players, but one that couldn't win when it mattered most.
"I think it's an opportunity to show other people around the country that this team had the talent the last two years, but maybe didn't have the maturity," Laurinaitis said. "I think this team has grown up a lot. Guys have battled and stayed mentally tough. We have a chance to go out and show people what this team is really made of. We'll be remembered for how this game plays out. It's a fact."
Mark Schlabach covers college football and men's college basketball for ESPN.com. You can contact him at email@example.com.