DALLAS, DEC. 31 -- After dominating college football for most of the '80s, Miami, ranked fourth and practically having to beg to be included in the national championship picture, found itself in unfamiliar territory on the eve of the Cotton Bowl.

The same might be said of No. 3 Texas, an arriviste that climbed above the .500 mark for the first time in three seasons. However, the Longhorns are too busy trying to live up to their credo -- "Shock the Nation" -- to realize it.

"My motivation has been the national championship since I was a freshman and now we're here," said Texas defensive end Oscar Giles. "This is the biggest game of our lives and now we're ready to knock off the team of the '80s and set ourselves up to be the team of the '90s."

On the verbiage meter at least, Texas (10-1) seems well on its way to supplanting Miami (9-2), which created media waves for years with its off-the-field antics. However, the Hurricanes almost always backed up their boasts, winning national titles in 1983, '87 and last season.

Whether the Longhorns, who have T-shirts proclaiming their intent to "Shock the Nation" and do "Whatever it Takes," will be able to do either beginning at 1:30 p.m. Tuesday remains to be seen, but Miami Coach Dennis Erickson said he's "scared" of Texas's capabilities.

"I watched the game between Texas A&M and Brigham Young {the Aggies' 65-14 rout in the Holiday Bowl} and I can't believe that Texas A&M was the second-best team in the Southwest Conference. Now we have to play the number one team," said Erickson, whose low-key style presents a marked contrast to Jimmy Johnson, whom he replaced prior to the 1989 season.

It was a 28-21 loss to BYU in the first game of the season that sent the Hurricanes into an eddy from which they have yet to recover -- and a win here still may not be good enough.

Miami lost to Notre Dame, 29-20, on Oct. 20 and even though it has won five straight since, the team can't seem to regain the attention of the pollsters. Tuesday, playing in one of the day's first contests, Miami has to win big and then hope for a Nebraska upset of No. 2 Georgia Tech as well as an uncompelling Notre Dame win over top-ranked Colorado to have any chance of repeating last season's title.

With a 29-22 loss to Colorado the only blemish on their season and victories over nationally ranked Penn State, Oklahoma, Houston and Texas A&M on their side, the Longhorns feel that -- with a Notre Dame victory -- they will belong on top of the polls.

The school hasn't played in a game with national championship implications since 1983, and that the current team fell behind in eight of its 11 regular season games, but none of this matters to the outspoken Longhorns players.

At a kickoff dinner here last week, tackle Stan Thomas called the Miami players "typical gangsters . . . I thought I was in prison. They're taking us lightly, thinking we don't play anyone but high school teams. . . . I was going to sit down at a table at the dinner and this guy said, 'Don't sit here -- I'm so-and-so from Miami.' I said, 'I never heard of you -- you must not play very much.' "

Miami averaged a school-record 325 yards passing per game and upon arriving here, wide receiver Randal Hill said he was looking forward to playing against a team that plays predominantly man-to-man defense.

"I personally like a one-on-one team; I haven't seen too much of it this year," said Hill, who had 44 catches for 653 yards. "Especially the bump-and-run that Texas tries to play."

That last comment brought a sharp rejoinder from Texas defensive back Stanley Richard, who said, "I guess they fail to realize that when they go deep, we'll be right there with them."

After the area was hit by a number of ice storms last week, conditions may not be right for an all-out aerial assault. Weather reports called for game time temperatures in the 40-degree range.

Even if the mercury doesn't climb that high, the Hurricanes say they won't be daunted by having to rely on the run. The ground game, which averaged 158 yards, was a key in Miami's crucial 31-22 victory over Florida State.

Texas averages 200 yards passing and 197 rushing. Running back Butch Hadnot, who led the Longhorns with 541 yards but didn't play in the season finale against Texas A&M because of a broken finger, is expected to be back in the starting lineup Tuesday.