I think she walked into Trump's trap. He dangled this juvenile argument out there, and Warren came at it the same way that Hillary did - she thought she was above it, and there's no way the American people would side against her on this school yard taunt.
She was wrong. The more she attacked it, the more the name stuck. And now it'll define her career for decades. Frankly, she has to go through this, and lose a few elections in order for her to be inoculated from it, at this point. She's not going to win this election (probably), but if she plays her cards right, she could set herself up for another run 12 years or so.
Politically, it's bad. But real world... come on this is nothing. Does anyone really think that she listed herself this way as some kind of strategy to get ahead? Like, "oh haha, even though I know I'm 100% white, I'm going to lie on these forms and no one will be the wiser!" No dude. The most likely answer is that she was taught that she was part Native American from birth. It was, in fact, the identity that she identified with the most... cause that's what she was told. And I don't see any tangible advantages that she's claimed as a result of this. It was a mistake. She deluded herself into thinking this fantasy about herself. Is that unforgivable? Does that really tell us something about her... that I'm not picking up?