I disagree with part of @JonMark's response. I feel the following statement in particular is a bit of a stretch/misinterpretation, given there's nothing in the context of the interview that would imply "the little bit" refers to a part of his brain:
'The little bit' is a reference to the part of his brain that is deciding whether or not to carry on lifting the weights.
I believe "the little bit" simply and literally refers to the last bit of the workout that's left. Other than that, he's basically got the interpretation down correct.
I did some digging around, and on Archive.org, I found a transcript of the interview in question, which aired on 60 Minutes:
Jackman sculpts both beard and body, and he invited us to his two-a-day workouts.
Jackman: That didn't feel easy this morning.
Pelley: Impressive. Impressive.
Jackman: I always say, when I lift something heavy, I remember that is wolverine. The little bit to where you're going to want to drop it and then you go, "no way," that little bit is wolverine.
Pelley: You change bodies the way other actors change costumes.
In summary, when Jackman says "That little bit is Wolverine", he's implying that the little bit of the workout that remains is reserved for Wolverine, that if he (Jackman) can't finish it, he has to enter the mindset of Wolverine and push through to finish that little bit of the workout. I like to think of it more as:
"This last little bit of the workout is all you, Wolverine."