Several Stanford football players watched TV in their locker room Monday as the three finalists for the Heisman Trophy were announced. Among those watching was Christian McCaffrey, and when his name was announced, his teammates cheered.

McCaffrey admitted he “got a little emotional.”

College football’s single-season leader in all-purpose yardage was invited to Saturday’s Heisman ceremony in New York City, along with Alabama tailback Derrick Henry and Clemson quarterback Deshaun Watson.

Stanford has just one Heisman winner, Jim Plunkett in 1970. Whether the school lands a second will be announced Saturday. The ESPN telecast begins at 5 p.m.

“I want to say how humble I am and how grateful I am to be put in this situation,” McCaffrey said. “The two guys I was named with are incredible players.”

The sophomore tailback and return man was barely in the Heisman conversation at midseason but made a strong push down the stretch. He became Stanford’s fourth finalist in the past seven seasons.

Stanford has produced more than its share of runners-up for the game’s most prestigious award. John Elway finished second to Georgia’s Herschel Walker in 1982. In recent years, the Cardinal had three more second-place finishers: Toby Gerhart (who lost to Alabama’s Mark Ingram) in 2009, Andrew Luck (to Auburn’s Cam Newton) in 2010 and Luck again (to Baylor’s Robert Griffin III) in 2011.

McCaffrey finished a strong case for the Heisman and other postseason awards by piling up 461 all-purpose yards — running, receiving and returning kickoffs and punts — in Saturday night’s 41-22 win over USC in the Pac-12 championship game. With 3,496 all-purpose yards this season, he broke Barry Sanders’ 1988 national record of 3,250.

“He’s gained more yards in one year than anybody who’s ever played college football,” head coach David Shaw said. “That’s something you can’t dance around. … It’s not just a conference record or just a really good year. This is a historic year. He did something no one’s ever done. And he’s done it better than everyone that’s ever won a Heisman. It’s phenomenal.”

Henry led the nation in rushing (1,986) and scored 23 touchdowns despite playing in an offense with an inconsistent passing attack. He broke the single-season SEC rushing record, an impressive feat, considering the conference’s rich history of running backs.

Watson, probably the top dual-threat quarterback in the country, led the top-ranked and undefeated Tigers to a 45-37 win over North Carolina in the ACC championship game Saturday, throwing for three touchdowns and rushing for 131 yards and two scores.

There are 929 Heisman voters, including 145 media representatives from each of six sections, plus 58 former winners and one vote that’s given to the public on an online ballot. The deadline for voting was Monday.

Shaw wouldn’t speculate on whether the Southern votes for Henry and Watson might be split, to McCaffrey’s advantage. The fact that Stanford played seven night games probably won’t help him, Shaw said. “Especially early, he was having some really good games but didn’t get a lot of notoriety because half of America is asleep when he’s doing what he does,” Shaw said.

With the Rose Bowl against Iowa still to come on New Year’s Day, McCaffrey is second to Oregon’s Royce Freeman in the Pac-12 rushing race by the thinnest of margins. McCaffrey has rushed for 1,847 yards in 13 games, an average of 142.1 yards per game. Freeman is at 142.2 in 12 games. Oregon plays TCU in the Alamo Bowl on Jan. 2.

Tom FitzGerald is a San Francisco Chronicle staff writer. E-mail: tfitzgerald@sfchronicle.com Twitter: @tomgfitzgerald

Season stats

Christian McCaffrey broke the record for single-season all-purpose yards this season — which doesn’t include passing. His stats before the Rose Bowl: