The last time TCU won a national championship in football was 1938. The Horned Frogs went undefeated that year, beating a school named Carnegie Mellon in the Sugar Bowl. Dutch Meyer was the Horned Frogs’ head coach. The legendary Davey O’Brien was the quarterback.

It’s taken 76 years, but the Horned Frogs are now within spitting distance of competing for another national crown.

TCU slid back into the top 4 in the College Football Playoff poll on Tuesday — and did so emphatically, leap-frogging the only remaining undefeated team in FBS, Florida State, and moving into the No. 3 spot. If the season ended today, the Horned Frogs would be playing Oregon in a national semifinal game.

 This is perhaps the hottest debate in the first season of the College Football Playoff: If the committee takes a Big 12 team, should it take TCU or Baylor?

That’s a huge win for a program that, just a few years ago, joined the Big East Conference in a desperate rush just to gain guaranteed yearly access to a BCS bowl game.

But the regular season doesn’t end today. It ends this Saturday, as the Horned Frogs host Iowa State, and the road ahead is fraught with uncertainty.

First, TCU (10-1) has to beat Iowa State. The Cyclones are 2-9 this season. The Horned Frogs should win, but you never know. Everyone thought Oklahoma State would beat Iowa State a few years ago, when all the Cowboys had to do was win to go to the BCS National Championship game, and the Cyclones won.

Then there are the things that the Horned Frogs can’t control. If everyone ranked around them wins this weekend — which is possible — theoretically the Horned Frogs should be in, right?

Not necessarily. And if that were to happen, the Horned Frogs might have that Baptist school down in Waco to blame.

Baylor, which has the same record as TCU (10-1), believes it has a claim to the College Football Playoff as well, if the committee is intent on taking one Big 12 team. The Bears are so adamant about it that they hired a public relations firm to help tout its credentials to the media. It’s a bold move, to be sure.

But Baylor believes it has one feather in its cap, all things considered — it beat TCU.

Yep, TCU’s only loss is to Baylor, a 61-58 track meet in Waco in October that, at the time, simply felt like confirmation that Baylor was the Big 12’s best team. Usually, people see head-to-head results as an indication of that very thing.

But not the College Football Playoff committee that meets weekly in Grapevine. No, this committee looks at TCU and Baylor, with their 10 common opponents, differently. Jeff Long, the Arkansas athletic director who chairs the committee, said on Tuesday that the committee sees TCU’s win over Minnesota — which finished the season with eight wins — and TCU’s five wins over teams with records better than .500 as indications that the Horned Frogs are better.

Baylor has a chance to improve its case this weekend against Kansas State, a team in the College Football Playoff top 10. A win for the Bears would give them four wins over teams with .500 or better records. A little chaos around them would help too, as the Bears are No. 6, in the College Football Playoff poll. Plus, if Baylor and TCU both win, they’ll have identical records and share the Big 12 crown, as the league announced it would not break the tie for the committee.

The committee has said in the past that it would give weight to conference champions, but not necessarily select teams based on such criteria. Normally conferences would use head-to-head to break these ties, so that would, theoretically, make Baylor the Big 12 champion.

This is perhaps the hottest debate in the first season of the College Football Playoff: If the committee takes a Big 12 team, should it take TCU or Baylor? Who would have thought that a half-dozen years ago?

No, a half-dozen years ago TCU was clawing for whatever scraps it could get out of the old system. It’s not quite win-and-you’re-in for these Horned Frogs, but it’s as close as they’ve been in generations.  One more game, one more win, and we’ll find out if these Horned Frogs have done enough to secure a spot in the first College Football Playoff.