Alongside its chase narrative, the movie examines two romances - that between Willie Boy and Lola, ie, the fugitives, and that between the Sheriff and a very curious character, a frontierswoman/doctor/anthropologist lady who runs the Indian reservation. It is the latter relationship that is really fascinating, and kind of horrible. It's sheer power play. It's like something straight out of Ayn Rand, actually, except taken up a notch. It's like watching a sort of train wreck, and it's so fascinating that the rest of the movie almost pales in comparison. But then there's this amazing contrast between the two relationships that becomes totally absorbing.
Oh man, it really is an amazing movie. Highly, highly recommended.
For those on Netflix, it doesn't seem to be available as a dvd (I saw it at my wonderful campus theatre, on 35mm), but it IS available for Watching Instantly.