Not sure how much of a chance she has. Would she get more publicity if she were a Democrat? She wouldn't be the highest ranking elected official of Native American ancestry, Herbert Hoover's vice president Charles Curtis was also of Native American ancestry:
American Indian officially enrolled within a tribe. We already have a Cherokee and Chickisaw...but they are republican men so..... After we get the first woman American Indian, then it will be the first gay Indian and so on.
No doubt if she was running as a democrat she would be above the fold so to speak on every news paper and network. Anyone that didn't vote for her would be labeled a racist plain and simple.