MIAMI - If the BYU football team thought it had an opposing quarterback with something to prove on its hands the last time out - when the University of Utah's Scott Mitchell convincingly displayed that he could have been an All-American Cougar - wait till they get a look at who's next in line.

The University of Miami's Steve Walsh has a story somewhat similar to Mitchell's. He's having a banner season and he's among the top-rated quarterbacks in America - but he has not beenturned into a household name. Not a whole lot of people know who he is. Like every other quarterback in the country this season, Walsh has had to take a backseat to the two Hollywood quarterbacks - Rodney Peete of USC and Troy Aikman of UCLA.

When the Heisman Trophy results are announced this weekend, it's likely that Walsh will be behind both Peete and Aikman in the voting, as well as the probable winner, Barry Sanders of Oklahoma State.

This, despite the fact he has had a better season. Going into the BYU game in the Orange Bowl tomorrow, Walsh, in just 10 games, has thrown for more yards (2,878) and more touchdowns (28) and had fewer interceptions (10) than either Peete or Aikman, both of whom have completed their full 11-game schedules.

Walsh's season is more comparable to Utah's Mitchell, who threw for 4,322 yards with 29 touchdowns and 15 interceptions in his 11-game schedule.

Walsh can put the finishing touches to his superlative season against the Cougars. He can also put a damper on the Heisman presentation in New York. And, for good measure, he can keep alive an outside chance of winning a second straight national championship.

In other words, if BYU was counting on a big-headed quarterback with nothing to prove for the last game of the regular season, they couldn't have counted more wrong. Better to have played Walsh and the Hurricanes the first week of the season _ as was originally scheduled until TV got into the picture _ than to meet them here and now, with so much on the line.

Since Walsh succeeded Vinny Testaverde as Miami's starting quarterback a year ago, when he was a sophomore, he has:

_ Won 21 games and lost one.

_ Led the Hurricanes over Oklahoma in last year's Orange Bowl for the national championship.

_ Put the Hurricanes in position to win this year's national championship if West Virginia could upset Notre Dame in the Orange Bowl.

_ And put himself firmly in line as a worthy successor to Miami's string of '80s quarterbacks that started with Jim Kelly (now with the Buffalo Bills), Bernie Kosar (now with the Cleveland Browns) and Testevarde (the Heisman Trophy winner, now with the Tampa Bay Buccaneers).

Still, the chances are good you've never heard of him.

No promotion campaigns have been mounted by the Miami athletic department. No hype has been pushed. And then of course, there's the long shadow cast this year by Peete and Aikman.

It's nothing new to Walsh. A native of St. Paul, Minn., he was lightly recruited out of high school, failing to attract a single offer from any nearby Big 10 schools. He came to Miami wanted but unheralded _ they thought he had the tools needed for a good dropback quqrterback _ and was promptly redshirted. During Testaverde's senior season in 1986, he threw two passes and completed one.

Nobody proclaimed him as the Air Apparent.

Miami Coach Jimmy Johnson concedes that Walsh doesn't have the raw talents of Kelly, Kosar and Testaverde. "But look at the real positive," said Johnson recently in The Sporting News. "Steve Walsh is a bottom-line winner."

Such is the way a coach talks of a quarterback who wins a national championship his first try and whose only loss in college was a 31-30 setback this year to Notre Dame in a game that could very well be looked back on as the game that decided the national championship.

In that game, Walsh rallied Miami from a 31-21 deficit to close within one point. If a two-point conversion attempt _ the `Canes were going for the win, not the tie _ hadn't been knocked down in the corner of the end zone with 45 seconds remaining, Miami would now be the front-runner for the national title.

As it is, Miami's only hope to win the mythical championship is for 11-0 Notre Dame to lose to 11-0 West Virginia in the Fiesta Bowl, and for Miami to convincingly beat Nebraska in the Orange Bowl.

And the `Canes obviously can't afford to blemish their record any further in tomorrow's regular season-ending game against Brigham Young.

Miami's Steve Walsh has accomplished a lot in his first two seasons as the Miami quarterback. But he has a lot left to prove. BYU couldn't be trying to hit him at a worse time.

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