I'm not worried about this team's heart. If anything, they've proven they have a lot of it through the first half of the season.
I am worried about the defense. I understand Southern Cal has a lot of speed and talent in their receiving corps, but it seemed like ND was playing prevent defense a lot of times. There were times when all a USC receiver had to do was run to the sticks, turn around, and wait for Barkley to hit him with no defender within ten yards of him.
In general, the secondary plays soft coverage too much. If you're going to blitz a lot, you better be able to disrupt quick timing routes by jamming receivers at the line.
As far as pass rush is concerned, I think you can break it down into two issues. The main problem is coaching. One of my biggest gripes with Oliver, when he was the d-line coach, was that the line rarely looked able to put pressure on the QB without help. I think it's still a little early to tell if Hart is the answer (I don't think he is longterm considering his age), but there seems to be a definite improvement along the d-line in recent weeks, especially in the run game.
The last major issue on defense is their inability to tackle. Too many times guys are going for the strip instead of just bringing the ball carrier down, especially in one-on-one situations. This allows the ball carrier a greater chance to break tackles and gain extra yards after contact.