North Carolina is definitely one of the best teams in the tournament, but it's very difficult to make it to the championship game. There are so many good teams in the tournament, and almost all of them are capable of beating each other. If the tournament was played out 100 times, North Carolina would probably make the finals in about 20 of them, so there is a good chance that the Tar Heels will make it.
In the first NCAA round, the Tarheels got off to a very rough start. It was a tense moment for people who had them in their brackets to go along ways. A number 1 seed has never lost to a 16 seed, and fortunately that did not happen, but at the same time, the Tarheels barely won their first game. That's not a good sign for how far they have to go in the tournament.
From what I have researched, I believe there is a chance the Tarheels will not make it to the Finals. There are plenty of other teams that are more motivated to reach the finals; teams that have yet to be there or teams that are on hotter rolls. There is nothing that I have reviewed that leads me to believe the Tarheels will make it to the Finals.
I think that UNC is going to make a good run, probably all the way to the Final Four. However, I think when they get there, they are going to meet UVA, and I really think UVA has a much stronger game than UNC. Time will tell, and it's even possible for UNC to lose in the next round. It's March Madness, where anything can happen!