by Billy Witz, FOXSports.com

When USC is welcomed into a packed Los Angeles Coliseum in a prime-time, nationally televised game Saturday night against Notre Dame, it's just the type of stage the Trojans need to make their case that they belong in the national championship debate.

Except that in this game, the Trojans can't win.

Look where all the contenders who are jockeying behind unbeaten Alabama will be this week. Oklahoma brings its Arena League offense to Oklahoma State, which pushed Texas harder than the Sooners did. Florida heads up the road to Florida State, which may be respectable enough to keep the Gators from looking ahead but not enough to bother them. And Texas, which can beat the stuffing out of Texas A&M, sits in the No. 2 spot and has the best resume of anybody — something that, Sooners or later, poll voters will come to their senses on.

As for USC, well, it needs a bailout like Citigroup.

The Trojans sit in fifth place in the Bowl Championship Series standings, much closer to No. 6 Utah than they are to No. 4 Florida.

It used to be that Notre Dame and a national audience provided the kind of oomph that could help a candidacy.

Nobody knows this better than USC. Carson Palmer's late season charge to the Heisman Trophy was fueled by a four-touchdown, 425-yard performance against seventh-ranked Notre Dame. Two years later, Matt Leinart used a five touchdown, 400-yard passing night against the Irish to edge out Alex Smith, Adrian Peterson and Reggie Bush for the trophy. That Notre Dame team was just 6-4, but had at least beaten two top-10 teams during the season.

With Notre Dame looking so dreadful this season, what could the Trojans possibly do to get a boost from this game? Offer to let Weis videotape their signals?

This is a team that just lost to Syracuse, which has been so bad it fired its coach before playing the Irish.

If Notre Dame was shut out by Boston College, what's the purportedly best defense in the country supposed to do — play with an arm tied behind its back?

The Trojans had their one chance to impress the voters in September and they held up their end of the bargain with a 35-3 whipping of Ohio State. But a week later, they lost at Oregon State and fell like a stone to ninth in the polls.

Ordinarily that wouldn't have been so bad. Ohio State dropped from No. 1 to No. 7 in November of last year and still made it back to the BCS title game. LSU came back from two losses to get there. The Trojans had two more months to work their way back.

The problem is they haven't had the schedule to do it. The Pac-10 has been dreadful this season, possessing a 1-5 record against the Mountain West. Oregon State is one win from heading to the Rose Bowl and though the Beavers are underrated, they were clocked by Penn State earlier this season and lost to Utah.

The Beavers' other loss was to Stanford, which has lost to ... Notre Dame.

Truth be told, USC hasn't always played like a national championship contender. The Trojans haven't really found an offensive identity, quarterback Mark Sanchez hasn't been consistent, and they commit penalties in Raider-like fashion.

Then again, who among the teams in front of them would really want to play the Trojans for the national title?

If Alabama's offense can't score a touchdown against Tulane, what does John Parker Wilson do against the Trojans? Does Mack Brown ask if he can bring Vince Young back for the game? When Bob Stoops had soon-to-be Pro Bowlers Adrian Peterson and Jammal Brown, and three future NFL receivers and still got blown out by the Trojans, what's he thinking now?

And that speed advantage that Florida enjoys over just about ever team in the country? Against the Trojans, it would be a two-team track meet.

Pete Carroll has been a master at preparing his teams for big moments and big games. He has won 22 of his last 23 games against teams outside the Pac-10 — and it's not the Citadel either. The Trojans have won at Nebraska, at Auburn, at Arkansas and played Virginia Tech in its backyard, Washington D.C.

Carroll has taken USC to the Rose Bowl or Orange Bowl the last six years, and won five times — all by at least 14 points.

The only blemish was the defeat to Texas in the national championship game in 2005, one that the Trojans were 19 seconds — or a converted fourth down — from winning.

The Trojans rarely have trouble when the stakes are highest and the spotlight the brightest, always seeming to rise to a big occasion.

Now all they can do is beat Notre Dame this week, dispatch UCLA next week and wait, hoping that one presents itself.